How much you end up sympathising with him is, of course, up to the interpretation of the audience. Either he was a pawn in God's/Jesus' plan, a pawn in the Pharisees' plans, or misguided but ultimately chose his fate. (Or a mix)
Word of God from Tim Rice says that his aim as far as presenting Judas' character was more to do with showing what he might have done in the same situation rather than making him interesting.
Pontius Pilate was also given some different perspective. In the musical he does not want to execute Jesus, thinking he is just another nut case who doesn't deserve death, and is utterly baffled why the mob wants him killed. He only goes through with the execution because he was given no other choice.
Though a similar impression is given in the Bible. That or not wanting to be bossed around. Many, many adaptations have been made over the centuries, in which Judas, Pilate, and/or the Jews have been blamed to a greater or lesser, sometimes very extreme degree.
In the 2000 film, even Jesus gets this; he comes off more than a little selfish in response to Judas in his early scenes, when Judas is protesting Mary's spending money on expensive foot ointments instead of the poor:
Jesus: There will be poor always, pathetically struggling; look at the good things you've got!
...You'll be lost, and you'll be so sorry, when I'm gone!
The 1973 version has him be more sad and solemn about it.
The Gospel of John, from where this scene is taken, says that Judas didn't actually care about the poor but only wanted to help himself to the money, as he was their treasurer. In the musical there's no indication he is anything but sincere.
Caiaphas comes across a bit this way, particularly if you know the history of the area. His interest is in preserving the status quo, not because the status quo is so good, but because the Romans will brutally put down any rebellions - like they eventually did a generation later when Judea rose in arms. Caiaphas is willing to sacrifice Jesus' life because he believes that doing so will save many, many other lives. This is fairly ruthless, but it's not evil or sadistic (as Caiaphas is often portrayed elsewhere and Annas still is here).
On a different note, whether or not Christ is actually divine is ambiguous. There is evidence both for (his prophecy to Peter and Judas) and against (Jesus running from the lepers instead of healing them, and his prayers in Gethsemane) in the music, and it is typically left to the individual production to sort it out, usually in Judas' "Jesus Christ Superstar" number and after Jesus' death, where some productions will throw in a hint that he has resurrected.
Awesome Music: The soundtrack topped the charts before the play came out.
First Installment Wins: Fans of the original LP concept album point out that it set the standard for all subsequent versions.
Literally, in the case of the vocal score, which in many places merely transcribes what was performed on the original album.
Ham and Cheese: Pilate tends to be played with either this or Tranquil Fury. Fred Johanson (2000) is an example of the former; Alex Hanson (2012), of the latter. Barry Dennen (1973) does both at different times, but errs toward ham, albeit with not as much over-the-top attack-dog viciousness as Johanson.
Worth noting is that Pilate's apparent one constant character trait is being out of his depth, and a lot of his characterisation comes from this. Barry Dennen's Pilate is relatively calm when we meet him in Act I, but becomes angrier and more vicious throughout the show as a result of the stress and strain of trying to understand and to dispense justice while knowing the crowd will lynch him if he doesn't give them what they want.
Meanwhile, Fred Johanson's Pilate is near tears from fear in "Pilate's Dream", but resolutely macho and hypermasculine when next we see him - the tears are his real self, while the borderline psychotic rage which characterises the rest of his performance is a facade of machismo put on to please the crowd and give the impression of strong, merciless leadership. Reinforcing this impression is the fact that in the lull just before the final "Remember Caesar" section of "Trial Before Pilate", when Jesus is the only person who can see his face, the facade falls and the rattled, extremely scared look from before is back.
Among the major portrayals, Hanson's Pilate is different in that he is negotiating from a position of strength; Dennen's Pilate risks being physically torn apart by the mob, while Johanson's Pilate risks an unsustainable loss of face. Hanson's Pilate seems to be better-protected, and as a result he remains relatively calm even up to the start of "Trial Before Pilate", when he begins to sense that things are not as they should be and that the problem will not blow over on its own. His eventual rage is not born of fear; it comes from bemusement, turning to frustration and helplessness.
Hell Is That Noise: The overture starting out the original 1970 album begins with an acid guitar lick with a sinister Asiatic purr (perhaps representing traditional Middle Eastern music) that can be very unsettling - even spooky - to Western listeners. And that's even before the "horror movie" synthesizer kicks in...
A few of the live productions play up the gentility and respect in their relationship - they're like brothers.
The 2000 version seemed to do this as blatantly as possible (some would say it was turned Up to Eleven). All the apostles wore tight ripped shirts, leather pants, and very frequently caressed and hugged each other. While the women all wore pretty modest ankle length dresses and their hair held in a ratty bun.
To compare, in the 1973 version Judas' kiss of betrayal is Judas sneaking up from behind, giving Jesus a very quick light peck on the cheek. In the 2000 version, the two are looking each other directly in the eyes while crying. Then Judas gives him a deep, long, smooch and Jesus responds by briefly wrapping his arms around him before Judas pushes him off.
In the 2000 version of "Heaven on Their Minds", Judas pleads to Jesus while they are alone together, with lots of Judas getting into Jesus's personal space, and hesitant, delicate touches to Jesus's bare skin. Compare the 1973 version of "Heaven on Their Minds" which has Judas overlooking the group from a distance and talking to himself.
And then there's the bit where the last straw before his betrayal was catching Jesus and Mary Magdalene in a compromising position.
It's also arguable that the 2012 arena tour does this to a greater extent than the 1973 film... Probably not the 2000 one though. Some of the looks exchanged between Tim Minchin's Judas and Ben Forster's Jesus (or even just glances in the general direction of the other character) could easily be classed as 'longing'. Add to that Minchin's heartbreaking reprise of "I Don't Know How To Love Him" during "Judas' Death," and the fact that during "The Last Supper" some of the apostles genuinely look as though they're watching a couple have a screaming row..
Caiaphas and Annas, oddly enough, also get this in the 2012 production. It's relatively restrained, but there are a few looks shared in quiet moments; most notably, in this production, Judas punches Caiaphas in the face in the "Damned For All Time" section of "Judas' Death", and Annas hands Caiaphas a small towelette to wipe off the blood, giving him a positively throbbing look as he does so. The height disparity (6'6'' Caiaphas v. rather diminutive Annas) and the distinct difference in manner (Caiaphas blue, Annas red) add to the impression.
Pilate: What is this new respect for Caesar? Until now it has been noticeably LACKING!
Narm: In the original album, during "Pilate and Christ" when a Roman soldier says "Someone Chrois', king of da Jeeewwwsss" in the Cockney accent.
The bizarre facial expressions made by Simon during "Simon Zealotes". The portrayal is less "violent, rebel agitator" and more "stoned, dancing hippie." Made even better by Judas' reaction shot, which can only be described as "What is this I don't even..."
You can even see Christ cracking up a little when Simon starts singing in his face. Corpsing?
It doesn't get better in the 2000 production, given Simon's frosted tips and the flamboyancy of some of his gestures.
The 90s Aussie production in spades. Strange Thing Mystifying sounds like a hair metal anthem.
The potential for Narm in "Heaven On Their Minds" is very strong, especially the first cry of "JEEEESUUUUS!"
Nightmare Fuel: The Crucifixion and preceding torture in the 1973 version.
The stage version includes a sequence so traumatizing that it's the visual/musical equivalent of swallowing an ice cube too fast. Immediately after performing the first half of "The Temple and Lepers," Jesus is accosted by a whole horde of lepers, cripples, and various other blighted folk. Pretty heart-rending in itself. But did I mention that they are covered in spider webs? That they're so wrapped in rags that you can't see their faces? And that they graphically describe all their injuries and infirmities in song? True, it's not Michael Jackson's Thriller, but it's pretty grotesque in itself. You can hardly blame Jesus when, in a What the Hell, Hero? moment, he screams: "HEAL YOURSELVES!!!"
Not forgetting that the song they're singing? It's the same tune as the merchants', only... different. And in 7/8 time, one of the most unsettling time signatures.
In the 1973 movie, the flogging itself is nasty enough, but then there's the intense music that goes with it, and Pilate's voice counting out the lashes. He sounds almost elated. Then when we see him trying to compose himself, he has an expression that could be aroused or disgusted or both.
The 2000 version has the look of realisation on Jesus' face when he is held down to the cross and sees one of the soldiers picking up a nail.
The brutality of the crucifixion having been foreshadowed during the 1973 movie's "Gethsemane", where the moment Jesus accepts his fate, there's a montage of zooms on images of his crucifixion as depicted in paintings across the years since.
Obviously Evil: The Priests in the 2012 version. They all wear suits (very much like investment bankers, in this Occupy-themed production), their council seems to take place in a boardroom, and their insignia (seen at the start of This Jesus Must Die) is an Eye of Providence (evoking the Illuminati) in a laurel wreath (evoking Rome). Caiaphas specifically falls straight into this, with his slicked-back hair and Beard of Evil.
Averted with Caiaphas in the otherwise fairly straightforward 2000 version, however. He has a relatively benevolent-looking face, as opposed to Annas, who looks almost exactly like Voldemort. Played straight by Pilate in the same version - he has a chinstrap Beard of Evil and his costume is a combination of a Gestapo officer and a Roman legionary.
Strawman Has a Point: Caiaphas and Annas are sitting on a powder keg (the people hate the Romans and are looking for any excuse to rebel) and see Jesus as the equivalent of a lit match in the powder keg. In Real Life, less than fifty years after the Crucifixion, the Jews did rebel...and got utterly crushed.