There are gaming benchmarks at the bottom. Maybe if you are lucky you can find your exact laptop model there. This is the video card Apple used in 2009 macbooks - so its pretty common.
Edit: Those are pretty new games, on a kind of old laptop. I'm betting most of them will need to be on lower graphic settings.
My current laptop (Core 2 Duo P8700 @ 2.53GHz, 2.87GB DDR2 RAM, Intel GMA 4500M HD IGP) can't even play Crysis or Crysis 2, or Battlefield 3, or NFS The Run. It can play SHIFT 2 Unleashed, but it only plays it at about 5FPS on lowest settings. I can play Skyrim on my current laptop, but the settings have to be at the lowest, with 800 x 600 resolution, and even then, I only achieve about 10-25FPS.
Will I notice a significant improvement in overall gaming performance compared to my current laptop?
Neither of these laptops are really good for gaming. Gaming laptops cost a bit more than this. The cheap way to game is with a desktop.
You will see a graphics hierarchy chart on the page I linked -- the 9600M is significantly better than the GMA 4500. The 9600 can play skyrim and Crysis on low settings. It's still not ideal for games.