When I built a PC 5 years ago, I put two 7800GTX's in, as Sli was all the rage at the time, a decision I have regretted ever since. The driver support (at the time) was flaky at best and restricts you to using one monitor.
I have recently built my new PC and moved over to a single Vapor-X 5770 and it is a great card, fast, relatively cheap, HDMI audio support and quiet to boot. However the driver support from ATi isn't great, I have HDTV issues (maybe solved with 10.1) as well as other issues, and overall I find the catalyst interface "clunkier" than nvidia's.
I disregard Eyefinity, 3D vision, Physx etc. as argument quantifiers as both companies will have these features like this in the future and they are all a bit superfluous to the main features and only used by a minority of people.
To sum it up I think this argument should be settled with driver support, as at the end of the day, both companies have made winning hardware in the past and as 3rd party vendors provide RMA and packaging etc. Driver support is the pivotal decider in my opinion.
I think that on the whole, nvidia tends to have slightly better support for their devices and consistantly release updates giving boosts to games released (I realise they fund a lot of these games, but I don't see this as a bad thing) and their cards are generally released with good driver support. The recent HD5000 Ati range (whilst being great hardware) was released without adequate driver support.
Sorry for the long post, but my $0.02
No-one has mentioned Intel yet, they have over 50% of the graphics market share!