That depends. If you treat it like it's a computer, and take care of it, it's not a problem. If you sit on it, regularly toss it into a backpack, drop things on it, hit things with it, and generally treat it like a rag doll, then you could have some problems with cracks.
I do none of those things and my palmrest has suffered cracks many many times. The Genius told me it was a design flaw, and even showed me what causes it to crack. The reason isn't related to mistreatment. It's due to picking up the laptop with your right hand, which is why most cracks I've seen reported in this forum are cracked on the right edge of the palmrest, not the left. Most people are right-handed.
Many other people have wrote concerns about the poly getting cracked. Is this a serious problem?
Yes, but only the very edge of the palm-rest.
I don't even have AppleCare, and Apple will still replace my palm rest for free. There's no reason to, as the part costs them nothing, and I'm pretty sure they know it's their fault, not mine. It's a bit of a hassle.
The rest of the laptop is pretty sturdy, probably much sturdier than aluminium. As a material, aluminium is a very soft metal. By "less sturdy", I mean the polycarbonate MacBook's ability to take a hit from something and resist real physical damage (i.e. not hairline scratches) is better than aluminium's. Same with older polycarbonate iBooks versus the PowerBooks from the past. I doubt that has changed over time.
The reason people say the Al Unibody MacBooks feel more durable is largely due to the new Unibody design process, not the material. This is also why you hear people say that the new unibody MBP is more durable than the old aluminium MBP.
Regardless of why the Unibody MacBook feels more sturdy than the plastic model isn't relevant, as there is no such thing as a unibody white MacBook.