Edge has had way more success than Christian, especially taking Christian's title reign that did not even last a week. Christian accomplished the one feat Edge never did though, he became a Grand Slam Champion.
Both Edge and Christian are this in regards to the Brood.
Dyeing for Your Art: Defied. When the Un-Americans were formed, management wanted Test and Christian to cut their hair into crewcuts to match Lance Storm - and to give the group a more militant appearance. Christian refused but he ended up cutting his hair a few months later anyway.
Money, Dear Boy: Numerous TNA talents confirmed that Christian left TNA when his contract expired and returned to WWE because the latter was offering more money.
Playing Against Type: In his first WWE run, Christian was almost always a heel. Even in TNA he came in as a face and quickly turned heel. In his second WWE run, he was a Face for the majority. Although he turned heel in 2011, he was back to being a face in 2012.
Real Life Writes the Plot: Maybe Christian would have gotten a legitimate WC shot soon anyway. But the Extreme Rules 2011 match where he won the title was supposed to be Edge defending his championship against Del Rio. But then, of course, Edge retired. This was even touched on by Michael Cole during the actual match - and he might have been doing it just to be stir things up, but he was actually telling the truth in a way. This then provided the next six months' worth of storylines, where Randy Orton won the belt five days later and Christian ended up turning heel over it.
Christian's TNA departure & WWE return - on both sides. If he had stayed in TNA, he would have become the mouthpiece for the faction opposing the Main Event Mafia; when he returned to the WWE, he was initially slated to be the person sabotaging Jeff Hardy's life, before everyone figured it out fairly quickly & the role in the feud was instead given to Jeff's brother Matt. Christian in turn went to WWECW and more or less carried the show until it was replaced by WWE NXT, to the point that he spent most of his return as ECW Champion up until the last episode of the show, where he lost it to Ezekiel Jackson in an Extreme Rules match.
Had Edge's body held out one more year, he would have had his retirement match at WrestleMania XXVIII, against Christian.