The Character Died with Him: Averted. Igor's role is diminished because of the death of his Japanese voice actor, but his archived dialogue from the game is still used to keep the character in the anime.
A bit of a peculiar case. In the English dub, while Johnny Yong Bosch voices our hero Yu, as well as Adachi (with barely much of a voice tone change from JYB unfortunately), the climax has these two characters going head-to-head. With Yu taking on a serious, powerful voice not unlike Bleach's Ichigo Kurosaki and Adachi using a lighter, maniacal voice not unlike Hollow Ichigo Kurosaki, insane laughter included, this showdown makes for a surprisingly familiar battle of the voices.
At one point, Adachi even says "You're such a pain in the ass...", an exact mimicry of one of Hollow Ichigo's lines aimed at Ichigo.
Naoto Shirogane's unidentified voice actor was replaced by Mary Elizabeth McGlynn.
Troy Baker is replaced as Kanji Tatsumi by Matthew Mercer, after the twelfth episode.
Playing Against Type: While the dub makes her more expressive, it's rather unique to have Cassandra Lee, who normally plays characters more impulsive and emotional, playing Aika, who is stoic, calm and rather serious.
The Resolution Will Not Be Televised: The TV broadcast only covered up to the "Good Ending", which deals with the confrontation with Adachi and the battle with Ameno-Sagiri. The REAL final episode, titled "No One Is Alone", was released with the tenth (and last) volume of the anime in Japan.
One of the things that convinced fans the series wasn't going to be a half-assed adaptation was the announcement that the entire cast of the game would be reprising their roles for the series. This even goes so far as to reuse Igor's dialogue from the game, due to his Japanese voice actor dying in the time between Persona 4 being released on & the development of the anime, rather than recasting the character.
The dub follows suit, to an extent - the majority of the cast returns, albeit with Johnny Yong Bosch altering Adachi's voice to sound less like Yu Narukami & the examples mentioned in The Other Darrin above.