Ok, I think I see where the disconnect is coming from. How about this:
Player 1: I want my character concept to be a fighter, a Master Swordsman, he's like Musashi, natural prodigy, trained by the best, lives his whole life by the sword, the absolute best anyone's seen in centuries. I want him to be able to pull off the Inigo Monteya hallway scene of cutting 4 guys down in one smooth movement that's so impressive the bad guy drops his sword and runs away.
Player 2: I want my character concept to be a fighter too, but a magic warrior, he's an eladrin and was in training to be a royal guard for the Seelie Court on the Feywild, but got out-maneuvered and was exiled. I want him to use magic to augment his sword-fighting, blade in one hand spell in the other, and help the party knowing all sorts of obscure arcane stuff.
Now, fast forward, both players have been playing their characters for ages and they're now both epic level ! Woohoo !
Let's say for example that Player 2's character is decent in his sword skills, and decent at magic. He's not as good with the sword as Player 1's character, and he's not as good at magic as a full-blown wizard. But overall, by mixing both together, he comes out as an equally capable character that can do a bit of both things. Player 2 loves this char.
Player 1's character is legendary, known far and wide as the best swordsman in the land. He can't fly like Player 2's character can (unless he gets a magic item to do that), and he can't meteor swarm like a wizard, but he can single-handedly take on an advancing army and turn the tide of a battle by wading through them cutting them down one by one and is basically untouchable by them. Player 1 is super happy that his char is awesome, and non-magical.
Question: What do you want Player 1's character to be able to do that he can't do? And why ?