All cards support VESA
Neither Nvidia nor AMD/ATI cards require their manufacturer's drivers to work, only to enable high-performance (3D) features. All VGA manufacturers support the VESA standards, including those two.
In addition, all major Linux distributions ship with non-proprietary/open source drivers for a dozen or so of the most popular manufacturers' graphics chips/cards (including the 'nouveau' driver for Nvidia cards). These are enabled automatically when the corresponding video chips are detected during installation.
So is there a difference between Nvidia & AMD/ATI when it comes to Linux? Actually, yes... Nvidia has a reputation for strong support for Linux, whereas ATI has given themselves a reputation of providing grudging support and releasing sub-par drivers. (If this has changed recently, and ATI users can vouch for improved support/quality for their hardware, please let everyone know... I only buy Nvidia for my machines; they all run Linux.)
