I'm compelled to weigh in on this one. Bernard is my favorite Knick and favorite player, and, of course, I'm his namesake for UltKnicks. I am also a Melo fan.
Bernard was more explosive. He was faster and much better on the break. He played harder and with more intensity and seemed more competitive. His low post turn-around was a pure, unstoppable go-to move. Thing of beauty. Melo doesn't have a similar go-to (not many do). Bernard had the best swish I've ever seen. He made the nets dance.
Melo has a better handle, is a better shooter from distance, is more creative and has more ways to hurt his opponent, is stronger and is a better rebounder.
They both play/played well against bigger guys. Bernard with his quickness and his ability to shoot his jumper on the way up, before defenders were ready to stop it -- Melo with his handle, creativity, timing and strength. They both can/could take over games for stretches where they are/were truly unstoppable.
Bernard's 60 point xmas game against the Nets back in, what, 83 or 84? -- 40 points in the first half, is up there with the best individual bball performances I've ever seen. One often sees guys go on rolls for a quarter at a time. That first half was just awesome.