The PSP version, Me & My Katamari, is coming soon in USA (don't think it's out yet), and I really have my doubts as to how it'll work without dual analogues. I doubt that thumb slider is going to be anywhere near as good.
Is the pushing mechanic similar to that on Billy Hatcher?
Hmmm...sortof, but not as irritating (I have to say, I hate Billy Hatcher with a passion. Tried to love it because it was Sonic Team, just couldn't in the end). Rather than you being able to drop your katamari like you would with the egg in Billy Hatcher, you're constantly attached to it, so you're not going to go dropping it. Rather than bouncing the ball up onto platforms, you get it as big as you can and push into things to move up to higher ground, climbing higher as you get bigger. Steering is also far easier.