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Well, you're asking to cover a lot in a brief forum post. Especially since it's a bit like comparing a sedan to an SUV to a pick-up to a minivan. They all have four wheels -- but which serves you best depends on your specific needs.
BTW, as I'm sure you're aware, Premiere Elements 9 is now available for the Mac too. So, although, at least in my experience, version 9 has fixed most of the bugginess of version 8 on the Windows platform, it also runs quite well on a Mac too. So that gives you another option.
Basically, Premiere Elements is a consumer program. It's got lots of pro features, but it's very user friendly and easy to work with.
Final Cut Express is just like Final Cut Pro, except without all the high-end features. Like FCP, Express can be challenging to learn. But, in my experience, I've not seen any bugginess with it.
Final Cut will digest pretty much anything you feed it. It also edits AVCHD very efficiently, since it does so using a proxy codec -- sort of a lower-rez preview file. The challenge is that this means that, when you want to output your project, it can take hours for the program to render it.
Both Premiere Pro and Final Cut Pro are used by professionals. Each has its own advantages. As I've said, Final Cut Pro has a lot in common with Final Cut Express -- but there are very few commonalities between Premiere Elements and Premiere Pro. They both edit video and look somewhat alike -- but comparing one to the other is like comparing a Honda Civic to a Mack truck. It's not really a fair comparison.
As for the bugginess you read about online -- I guarantee that there's not a program or computer system in the world that SOMEBODY hasn't reported issues with. The only true way to know if a program will work on your system or not is to download the free trial.
So -- if I can use the car metaphor one more time -- give them all a test drive. Only you know what's right for your needs.