I think they're similar.
Playing Doom 3 isn't the only reason for buying a fast 3D card, but see
here:
http://www.extremetech.com/article2/0,1558,1634115,00.asp
The article probably doesn't list exactly the model you are considering, but
a GF 5900XT may not be much slower than a 5900 Ultra. (If the 5900XT is like
other nVidia cards, it can easily be overclocked up to near the stock
performance level of the faster card.)
One warning: if you get a 9800, make sure that you get one with the full 256
bit memory interface. Some 9800 Pro models have the 128 bit interface (don't
confuse this with the amount of onboard memory, in megabytes: this is the
width of the memory bus). The 128 bit models are still fast graphics cards,
but their performance suffers, particularly at higher pixel counts.
(I believe that there may also have been a 128 bit version of the 5900, but
they may have all carried the SE suffix. Give them a miss as well.)
The least expensive choice would be a used card, if you can live without a
warranty. The Radeon 9700Pro isn't much inferior to a 9800, for example.
Finding a new one at a reasonable price may be difficult, but there must be
thousands out there that have been replaced by Geforce 6800 or Radeon XT800
cards.
Have fun.
Address is scrambled. Replace nkbob with bobkn.