Honestly, either of those cards should play STO fine. STO does show bias towards nVidia however, and quite a few other new releases do as well, so that would favor an nVidia card as well.
As far as what kind of power you need to run STO....I'm running a 5 year old 9600GT over clocked and STO plays at 35+ FPS in almost every zone with everything maxed except AA (2x) and the Occlusion thing at 1080HD (1920X1080). Some particle effects cause intermittent lag in ground environments, but no problems in space except for the bright light patches in Borg events. Sure 35+ FPS isn't exactly stellar, but its more than sufficient. So, STO is not exactly a system killer, and whatever you pick should do you just fine.
Note: STO ship battles are SPECTACULAR on a 50" LED with a good surround system.