Games run on Windows 7 better because Windows 7 can mimic the same conditions of a computer that runs xp or vista. The problem with Vista is that a lot of things had to be made compatible with it, Windows 7 doesn't have that problem at all.
So yes, it will help. It also is a lot more intuitive and finds drivers very well. In layman's terms that means it won't be necessary to do anything other than just install the game for it to run.

Get windows 7.  Here comes the marketing the mumbo jumbo: it's streamlined. It'll make you less angry. It'll probably use less resources than Vista, leaving more for your "game".

If you can keep yourself from falling for fancy new UI you'll probably save yourself a lot of headache with game compatibility. Lots of people report problems with it. It was the same deal with XP. Try waiting for few more months, wait till it gets more momentum and support.

If you want to run games better, why not downgrade and put XP on it. Windows XP uses fewer system resources than Windows 7 which uses fewer system resources that Vista. If you're just looking to get the most out of the hardware you already have, that may be your best option.

Windows 7 runs flawlessly for me, the only problems I have had were hardware related, its the best Windows OS I have used since 2000. (XP became good but when it was new it was a mess as well)
 
@raddevon: "
"The good news is that you won't have to spend long agonising over the whole 'XP or Vista?' decision, because Windows 7 generally outdoes them both. Microsoft really does appear to have learned its hard-taught lessons and, while it hasn't fixed everything, the latest incarnation of Windows does show significant improvements over its predecessor – impressive for a pre-release version. The finished Windows 7 can only be better, and it should finally give long-standing XP fans a reason to upgrade."
 
-Taken from TechRadar article.
 
It may not win in every category but Windows 7 Is the better of the two and if you have newer hardware XP would drag you down.

Honestly I'd recommend sticking with XP til more games start using directx11 and a service pack gets released. Or... you could... you know... yarr...

Games have no performance benefit on 7. Most tests show maybe a 1% benefit but that's within the realm of random variation; the largest difference I've seen is 10% in L4D and Far Cry 2 but the results are varied depending on the publication, here's one for example  http://www.maximumpc.com/article/reviews/windows_7_review?page=0,3 (you'll notice that the performance benefit is inconsistent across quality levels). That said, Windows 7 does offer about a 10% faster desktop experience, and cleans up a lot of unnecessary proceses for hardware-limited computers such as laptops. I've also fallen in love with its taskbar. 

" Games have no performance benefit on 7. Most tests show maybe a 1% benefit but that's within the realm of random variation; the largest difference I've seen is 10% in L4D but the results are varied depending on the publication, here's one for example  http://www.maximumpc.com/article/reviews/windows_7_review?page=0,3 (you'll notice that the performance benefit is inconsistent across quality levels). That said, Windows 7 does offer about a 10% faster desktop experience, and cleans up a lot of unnecessary proceses for hardware-limited computers. I've also fallen in love with its taskbar.  "

wow nobody's addressed your question.
 
Honestly Windows 7 is alot better then vista (it's not just a new skin, they've actually changed a few things to make it run faster) but from what I'm gathering your laptop doesn't have a good graphics card. So the short answer is no. So contrary to what others might tell you, if your game ran like crap in vista chances are it's not going to magically run smooth in 7 .
 
99% of the time it's a hardware limitation not a software. And anybody who says stick with XP is just....man i don't know. There seems to be this unbias love of XP and it's really unfounded. XP is 10 years old and it's plainly obvious. If you have the resources to run Vista, Vista will run better the XP. That being said Vista is a resource hog. Windows 7 corrects that and shines above XP, but it won't make up for your lack of hardware power (nor will XP). So I'd say upgrade to 7 regardless but don't expect a crazy boost in performance.
 
EDIT: Geno did answer it as well.

Based on my opinion and experience with Windows XP, WIndows Vista, and Windows 7, you probably wouldn't see enough of a performance difference to bother. Since all the updates to Vista, it has become a much more streamlined OS. It doesn't have the issues with running on slower hardware than it did when it was first released.  Yes, Windows 7 is better in every way, but not enough so that I'd suggest anyone plopping down the money on the upgrade unless you can get a significant discount (I bought it back when it was $50 a pop before launch).
 
If you're that worried, isn't the Windows 7 beta still available through March or June or something?
 
Also, to anyone suggesting that running WIndows XP might be a boon, I can assure you that the performance and features in Windows 7 make XP feel like a child's toy of an OS. That makes sense given that XP is 9 years old now, and technology has changed a lot since then.

I made the upgrade to Win 7 pretty close to release and I love it so far. It is fantastic, especially compared to Vista. I think it's almost as good as XP was.  
 
It's way faster and the kernel is quite a bit smaller than Vista's is so it'll leave a lot more of your system's resources for your games. I'm not a huge PC gamer, but from what I've heard it's way better than Vista ever was for games and no one has had any compatibility problems that I've heard of. 

for everyday use you will probably see a nice improvement over vista but you wont notice much in terms of game performance.
 
laptops are not ideal for serious PC gaming

Get a new laptop. New OS is going to change anything.

yes

 
Install XP.

" Get a new laptop. New OS is going to change anything. "

7 is great. No reason not to.
 
Also it is very very very easy to acquire freely, as I did it for my backup PC. And being I purchased Vista for less than a year as well as Win7 Pro upgrade DVD, I am entitled to it.

I'm thinking of upgrading from Vista too, as I understand it Windows 7 uses less RAM freeing up more for games?
 
I'm thinking of doing this specifically for GTAIV because despite meeting all the requirements it still runs like shit with everything on lowest settings.

Windows 7 is actually slower than Vista in games, primarily due to the fact that the GUI is loaded into the GPU memory so save on system memory usage, but its only slower by like 1 or 2 frames per second.  Over-all windows 7 is a much nicer experience, the UAC is much less in your face as most peoples biggest gripe with Vista was how invasive to the user experience UAC was.  Additionally your going not going to run into the same driver and compatibility issues people had when Vista launched as W7 is basically just a refined Vista framework, means all the growing pains from moving to the new framework were worked out during Vista's difficult transition from the old Win NT/2000 framework which XP used.
 
As it is if the laptop is old and all your playing is source engine titles just stick with XP until you get a new machine, source isn't a DX10/11 engine and odds are your laptop doesn't have enough grunt to handle those API's anyway.