The only real difference is warranties for the most part. The only company that I've seen any reports of model-wide shortcomings recently was from MSI in the 570 and 580 lines. Would probably recommend avoiding MSI's high-end nvidia offerings for the time being based on this, but everyone else has been producing roughly equally dependable cards recently.
Well, there are 2 major graphics chip makers, AMD and Nvidia. AMD is good for lower end gaming since they are normally cheaper and have the better performance, but once past a certain point, Nvidia wins. They don't produce their own graphics card though, they have other companies do that for them, such as: XFX, Gigabyte, ASUS, Sapphire (AMD), EVGA (Nvidia). There really isn't a "best brand." Since all AMD Radeon 6870's will perform similarly. You just have to choose between the different brand's warranty and Heatsink and fan. I would go with Gigabyte, XFX, and Sapphire for AMD, and Zotac and EVGA for Nvidia. I would also go with ASUS for both of them