I find it interesting that Tony Stark took the pro-Registration side, and Steve Rogers the anti-Registration one.
One or two escapades aside, Roger is a soldier, and one who fought in a huge, complex war that was probably the largest endeavor in centralized human and logistical coordination the world had ever seen. He knows how to give and follow orders and, most importantly, he knows when and why that works. In terms of his training and experience, it would make sense for him to say Look, I know SHIELD ended up being crap, but if we're going to keep fighting these wars, we are going to need to be part of the defense strategy. We can't always count on spare helicarriers to evacuate civilians — these things take planning, and Tony's expense account might look a bit like the US Government's defense budget, but in fact isn't.
And Tony... Tony has never, ever, ever followed anybody's orders. Hell, he spent an entire movie giving the middle finger to the American defense forces when they asked him to share his toys, and the first thing he ever did when he boarded a helicarrier was make fun of Fury. The second one was to hack SHIELD. This is not a guy who thinks he's more effective when some General somewhere tells him what to do, and he's definitely *not* a guy who thinks they have the right to, anyway, despite the fact that his brain is a WMD nobody has yet figured the firing control for.
I think each of them takes the opposite view, in essence, because of class issues. Tony, basically, sees himself (and, to a large degree, is) above the law (I mean, he's a rich famous white guy with a mechanized suit, what more do you want?). He's not worried that the Government will make him to do anything that'd compromise him morally, because he's prepared — and this isn't Machiavellian planning, that's just his default assumption — to ditch them the nanosecond they ask him to. Steve has already gone through that experience once, and went rogue, but not because he thinks laws are optional when they refer to him. He doesn't see himself outside the law — in his mind, his fight against SHIELD was about protecting the law, which is very different from Tony's attitude — so he's not going to support a law that puts him in that position again.