Everybody thinks that way, but in the reality he had full power in Advent Children. Kadaj was a remnant of Sephiroth. Yes, he wasn't as strong as Sephiroth, and he's body wasn't the same kind, but nevertheless when he put Jenova cells in him (not S-cell's, that was Jenova head he put inside of himself) he became Sephiroth, in all terms. He was able to summon that black sky, and it's not like he used in Crisis Core something else than blade attacks, so your argumentation is very off.
Oh, and Sephiroth didn't die in Crisis Core, he died when fighting Cloud in Northern Crater. Play the main game (Final Fantasy VII) before trying to prove something. It's the main game that matters the most.
As to the fight scenes, the one with Cloud is better, simply put it's more intense and the scenery and place where they are fighting is epic. It's not on a static place like cannon, it's between the falling pieces of Shinra building. That is epic and you can't deny it.