Both brand names have issues unique to each card. I can't say for sure which brand is better. Certainly ATi Radeon Cards are getting a lot of attention now because of CrossFire which, on certain boards can allow up to 4 Video Cards...
However, I will say this, on a lot of older games, both have had issues. I've been trying to remember whether or not the stuttering issue I have been having on Sim City 4 was there before I did a fresh install of Windows XP and popped in an ATi HD3450 as an upgrade to an Nvidia GF7200. I have both the 7200 and a 7300 sitting to the side so when I feel like finding out, I can swap the ATi Card out...
However I will say this on the X1000 series ATi Cards. Certain Games (Like Sims 2) were having issues with those. Sadly the same is true for many newer cards and older games.
Of course, with NVidia you get tech that ATi doesn't have but eh... They're the only two players on the field worth watching right now just like AMD vs Intel in the CPU arena...
You don't seem to know all that much about computers... What Games are you trying to play anyway...
Edit: I got your message. However, the way you talk... Well, that is why I say it doesn't seem like you know a whole heck of a lot and with you coming off of the Mac bandwagon... Well, ya know...
Anyway, like I said, there have been driver issues, especially with the most recent ATi drivers as well as the ATi X1000 series cards. Yeah it may be newer than the 9250 (which I have also owned and gave to a family member when I'd upgraded) but it had some issues that the 9250 didn't. Now as to why you're asking about this here when you probably should be on a tech or gaming forum asking since you apparently know a lot more than it seems like you know.
At the same time, I'm still perplexed. You probably shouldn't even be running those game on either of those cards. Unless of course you've got the specifics of the cards wrong... Like I said, it's hard to understand what you mean... What versions of the Cards do you have? If my memory serves me correctly the 9250 was primarily an AGP 8x card, but the X1000 series came out when PCIe was first catching on so there are both AGP and PCIe versions... Have you tested this on multiple system configurations?