Interesting topic. Too bad the two bands under scrutiny are totally different, even though they are labelled (by some) as "progressive metal."
Anyway, I'm sure this has been said a million times before in this thread, but even though Dream Theather may have more technical sound players, they, in my opinion, are the inferior
band. The members of Tool know when and how to compliment each of their songs, and they do a damn good job of it. Whether you like the music or not is a different story. However, you cannot deny that each member of Tool is a great musician (not saying that the Dream Theater guys aren't.....except for La Brie....he simply blows

).
Looking at each "position" individually:
Jones vs. JP: While JP is definitely a much more flashy player, Jones really creates some beautiful soundscapes and is very "artistic" in his playing. He doesn't really show off/max out his skill because the music doesn't require it, which deserves a lot of respect. However, JP, simply put, is a frickin amazing guitarist and really holds his band together (IMO).
Justin vs. Myung: Myung can shred, but come on, his playing is so boring and uninspiring. I mean yeah, some of those really fast tapping and solo parts may really impress you, but (again, IMO) he cannot hold a candle to Justin in terms of providing a backbone (and awesome riffs) to the song. I mean heck, you can't really even hear the bass much in a lot of DT songs. If you take out the bass from a Tool song, you've taken out a
whole lot. Chancellor is "better," no contest.
Maynard vs. La Brie: No contest here. You've got to be kidding if you think La Brie can sound anywhere as good as Maynard. Both have good lyrics, but Maynard's appeal to me more. Singing wise, James gets blown out of the water. With the exception of a handful of songs where he actually does sound good, La Brie either sucks, or is mediocre (at best) on everything else. Have any of you seen DT covering Master of Puppets live? If not, save yourself the agony.
Danny vs. Portnoy: Both have beastly chops. No question about it. But Danny knows when to use them more effectly (i.e. not in the middle of vocal melodies). Besides, you don't have to have terribly complicated parts to be a good drummer (which both do, but Portnoy at times seems to be excessive).
Tool vs. Rudess: Even though Tool have no keyboardist, they still do a great job as a whole in creating some awesome ethereal sounds. Rudess is an amazing player and can solo like a madman, and yet when it boils down to it, he can do some "background" sounds when needed. This is a pretty tough comparison since both "jobs" have totally different requirements, but I'd have to give the edge to Rudess for being more "versatile," so to speak. But then again, the Tool guys really go outside the box when doing what it is they do when they're not playing your tradition bass/guitar/drum/vocal "licks," if that makes sense.
Anyway, when it all boils down to it, everyone will have his/her own opinion (duh), so everything I just said really doesn't matter.
But yeah,
Tool for me.