If you're looking strictly at pure gaming performance, parts from either AMD or NVIDIA are going to be suitable for you (budget notwithstanding.) In the interests of fairness we'll include Intel in the pro and con conversation.
AMD vs NVIDIA vs Intel Mobile GPU
First, Intel has the best dedicated video encoding hardware on the market. AMD vs NVIDIA both offer solutions that allow you to harness their shaders to substantially accelerate video encoding, but Intel's Quick Sync is best of breed (behind pure CPU-based encoding), offering a healthy improvement in encoding speed while producing the best output short of doing encoding on the CPU itself. It's worth noting, though, that NVIDIA solutions and AMD ones supporting switchable graphics can take advantage of Quick Sync, so you don't necessarily have to tie yourself down to Intel to benefit from it.
If you take video encoding out of the equation, unfortunately AMD isn't quite as strong in terms of feature offerings, boiling down to arguably slightly better image quality and support for Eyefinity (provided the notebook has a DisplayPort.) They do have a hybrid graphics solution similar to Optimus, but availability is spotty and you'll have to research the notebook model you're looking at to see if their switchable graphics are supported. NVIDIA's Optimus on the other hand is pervasive and mature, and their mobile graphics drivers are more widely supported than AMD's. 3D Vision, CUDA, and PhysX are much more niche, with AMD also offering 3D support and materializing in 3D-ready notebooks. If you have a need for CUDA or a desire for PhysX, your graphics vendor has been decided for you.
Knowing what each vendor offers, now we just have to know what to look for.
The netbook or ultraportable gamer is pretty much stuck with either buying a netbook with AMD's E-350 processor or paying through the nose for an Alienware M11x (spoiler alert: heavier than most "netbooks.") That's not a horrible thing as the E-350 has a capable graphics core, but even though the CPU side is faster than dual-core Atom it's still not quite enough to pick up the slack.
Gamers on an extreme budget used to be more or less screwed, but thankfully that's changed. Notebooks with AMD's A6 or A8 processors are going to be your one-stop shop, offering a tantalizing mix of middle-of-the-road CPU performance with remarkably fast integrated graphics hardware. There's a reason AMD refers to the A6 and A8 graphics hardware as "discrete-class" and for once it's not just marketing jargon. If you want to game for under $600, this is the way to go. In fact, it's even a little difficult to recommend spending up for a notebook with anything less than a GeForce GT 540M or Radeon HD 6500M/6600M/6700M unless you really need the faster CPU on top of it. If gaming while on the battery is important to you, then you need to be looking for Llano.
Users looking for a more well-rounded notebook would probably be well served by the aforementioned GeForce GT 540M or Radeon HD 6500M/6600M. These will hang out between about $700 and a grand and notebooks using these chips are going to be fairly mainstream in form factor, so you won't be lugging a land monster around. Be forewarned, though, these GPUs are going to be inadequate for driving games at 1080p and may still struggle at 1600x900.
The serious gamer looking for an affordable machine should be gunning straight for notebooks with NVIDIA's GeForce GTX 560M. This, or AMD's Radeon HD 6800M, will be the bare minimum for gaming comfortably at 1080p, but honestly the GTX 560M is liable to be the sweet spot in offering the very best balance in form factor favoring performance before you start getting into the huge, heavy desktop replacement notebooks.
Finally, for those who money is no object to, just about anything from the Radeon HD 6900M series or the GTX 570M or 580M is going to do the trick, and for the truly excessive users, an SLI or Crossfire notebook will yield dividends.
