I've always had easier experiences with nVidia in Linux. However, haven't tried in a few generations with ATi. I can tell you the 4xxx series with linux almost drove me to insanity just getting any type of graphics acceleration to work with it. It's was more rediculous than setting up the old Intel GMA 950 series to work at all with Debian. Command line FTW! Either way, you can't go wrong as even if you do have a little trouble. Learning how to overcome a challenge is well worth it in Linux. Every time! The nVidia 4400Ti was one of the hardest nVidia chips to get to run under Ubuntu for the time. You actually had to rebuild the kernel with nVidia official drivers and compile! Took about a week of time to finally perfect but the adventure was great!
Ubuntu has a lot more problems with nVidia than AMD. I've never had a problem setting up a system with an AMD card. Multiple problems with nVidia over the years. Just a few days ago installed 12.4 on an old AMD motherboard with a nVidia 8600 and after updating the drivers the screen went haywire, not showing the icons or top menu. Reinstalled and used a different driver and it finally worked.