Believe me, Ive tried both. This is the way that I've always did.
Download the driver from AMD. Install some dependencies like fakeroot and stuff. Create the packages for Ubuntu/precise via terminal (fglrx, amdcccle, dev). Install the packages with "dkms -i" and finally "sudo aticonfig --initial -f". This is the way it always worked for me.
Well, it didnt work, so I remove them from Synaptics (the same way Ive always did too). Then tried the synaptics fglrx packages. Did not work either
Im using Ubuntu 12.04 32bit Gnome shell, and cant remember the Kernel, it is the one who provides the updates manager
Next time, when something doesn't work on AMD, because of NV drivers... Yep, NV drivers allow developers to write bugged code which will not work on AMD. I know that this is funny situation, but I know what I say, AMD drivers are more times better when we see at point "compliance with the ogl specification without vendor BONUS, which are vendor dependent...". I hope that in future Gnome Team will debug Your code on both AMD and NV cards or on AMD only, because now it looks like they check it only under NV cards (which is very bad solution).
Maybe for end user NV drivers under Linux are betters than AMD, but for programmers situation is different (only when You knew an ogl specification very good, You can use NV cards, but mistake is a normal thing, so I still think that AMD is a better choice for this job).