They all move relatively the same, but each class does have different jumps.
With the builds we're allowed to play with, they are as follows:
The Hunter has a cool Double Jump that can be upgraded into a Triple Jump with enough playtime.
The Warlock jumps and sort of hovers in the air which is a good way to get above the battlefield for a short while.
The Titan jumps very high and floats upward like he's wearing a jet pack.