Vista's big problems vs. Win7
1) Drivers. Driver model changed from XP to Vista. Lots of devices at Vista's beginning either didn't have drivers or had buggy/crappy drivers. Win7 uses Vista's driver model, so most Vista drivers will work on it. And since Vista has been "gold" for almost 3 years, drivers exist for most devices made in the last 4-5 years. (Past that, well, still good luck. If a device was really popular or the device/chipset manufacturer is good, maybe you have drivers.)
Note that this may changes a LOT if you go from 32-bit to 64-bit. 64-bit drivers may or may not work well on your system. My personal experience was with a Toshiba Satellite laptop. Utterly unstable BSOD city with 64-bit Win7, even with official drivers. Installed 32-bit instead and the system is rock solid stable. I'd rather be running 64-bit, but not if the system becomes unbootable within a day.
2) File copying. For me, pre-SP1 Vista was completely broken just for the file transfer issues. Transferring files to/from my corporate network took 20x (more?) that of XP. Completely unacceptable and a total deal breaker. (And I don't know how or why this critical bug ever escaped beta. Don't people at Microsoft actually transfer files on their networks???)
3) Performance. Vista was significantly slower than XP, and was pushed onto machines that were completely overwhelmed by this. Even more "hefty" systems struggled. The internal memos on this at Microsoft were classic. People bought $2000 laptops that were much slower than their 2 or 3 year old previous laptops. Vista performance stank. And RAM requirements were underplayed. XP runs fine with 512mb - 1gb of RAM (depending on your usage). Vista needs double that, but some of the original Vista systems had only 512mb.
Vista after SP1 (and some more updates) improved quite a bit on it's performance. Win7 is faster than Vista as well. OK, it's not as fast as XP. But the gulf between XP and Win7 is nowhere as vast as that between Win XP and Vista back in 2006-2007.
We're also 3 years along with Moore's law. Dual-cores are common. Some even have triple and quad cores. Graphics cards are much better as well. So average system power is much higher and more capable of shouldering additional computing burdens.
So Win7 should run well on most 2007+ systems (except for lower-end netbooks), especially if you up the ram to 2gb. Ram is dirt cheap these days, and almost all systems come with at least 1gb of ram. Even many consumer systems sell with 2gb or 3gb of ram.
I still wouldn't try to use it on anything other than really high-end "workstation" systems from pre-2006 (e.g., got a Dell Precision with dual socket Xeons?).
And if you bought a low-end early non-dual core Vista laptop -- sorry, just downgrade the system to XP. You got screwed.
4) UAC. Yes -- UAC sucks, especially if you need to do any real adminstration on a Vista system. I setup group policy on my corporate systems so that any administrator accounts had silent elevation, so UAC still ran but silently in the background. For home systems, sometimes I just turned the annoying bugger off.
It's easier to tone it down in Win7. At these levels, it doesn't pop up constantly, and probably is no more annoying than security prompts in OS X or having to sudo everywhere in Linux.
5) The UI.
And yes, I've been using Win7 on my laptop for a month. I'm still not completely happy with some of the UI changes vs. XP. (Vista of course had the same problem. Microsoft broke design conventions that existed since Windows 3.0 or so. Vista made items harder to reach -- requiring 5 clicks instead of 2 or 3. And so forth.) But the UI in Win7 is more polished and less annoying than Vista. I still miss the classic start menu, but I'm missing it less and less. And I couldn't live without the Quick Start bar. It can be somewhat easily faked in Win7. And no, pinning icons to the task bar is not the same -- they take up lots, lots more screen real estate.
6) Program compatibility.
We're better off here vs. 2006-2007. Most programs updated in the past 3 years and newer/updated versions run fine now on Vista. And if something runs fine on Vista, it is nearly guaranteed to work fine on Win7.
If you still have annoying legacy programs then yes, you'll still have problems. If you have the capabilities, test your older programs against Win7. Or run Win7's XP Mode and use that for legacy programs. Or even better, run a XP VM using VirtualBox -- higher performance and better system compatibility.
Overall:
So unless your Vista system was one of the early ones that had completely underwhelming horsepower (and you "upgraded" it to XP, right?), you should probably upgrade to Win7. But your 6-year old XP system? Stick with it or buy a new system with Win7 later.
If you're more conservative and you're not buying a new system, wait 3-4 months for Microsoft to update any inevitable bugs. And if you're really conservative (e.g. let's upgrade piles of corporate systems from Vista to Win7), wait a year or so until Win7 SP1.