My previous laptop (Dell 1535) had an ATI card. I used to run this laptop with an external monitor attached. With Vista's Aero feature enabled, my laptop would BSOD. Daily. Apparently this is a very common problem with ATI graphics chips in laptops. Thankfully I didn't actually need that feature, and was able to resolve the situation by disabling it, but it took over a year (and multiple MOBO replacements by Dell tech support) to discover this.
The problem was probably Dell imo and my money would be on a firmware or driver issue..
AMD (formerly ATI) and Nvidia for many years had their hands tied with laptop manufacturers who requested that they do not offer support for their device in the reference Catalyst Driver. So you had to rely on the OEM taking the reference drivers and modifying them etc. OEM's are pretty slack and never keep up to date with Nvidia and AMD who regularly release new drivers typically every month or quarter.
Recently both Nvidia and AMD got fed up and started including support for all gpu's in the mobile reference drivers. They made the system opt out instead of opt in, some OEM's still opted out!
Anyway nvidia is not immune to mobile gpu problems, they had a whole series that was defective and overheated a few years ago. When they finally admitted the problem their stock took a big tumble.
With Nvidia vs AMD and Intel vs AMD my advice is to just go for the best bang for buck at whatever price point you're looking at because all software has bugs, some hardware series has faults... often past issues aren't a good indicator of future problems.