Since the whole thing's fucked now, I might as well say what I really think about the first two. I only listen to The Mars Volta if I just want the silence to be drowned out. They're not really worth my time.
Dream Theater I just seem to not like at all. I couldn't stand their singer before food poisoning, or after it. Their songs generally consist of everyone taking turns playing solo bits, which I can't fucking stand. Everyone I've known personally (which excludes people from the internetz) that is a fan of this band thinks that everyone in it is a living god when it comes to playing their instrument/singing, which is just not the truth. I know they're a prog-metal band, and prog-metal bands are supposed to incorporate tons of musical theory into their songs, but that's only half of the process. You still have to attempt to write something with a catchy phrase. Basically, I hate Dream Theater for the same reason I hate a lot of prog-bands, they pile on the theory and not a whole lot else. Don't get me wrong, they're good at what they do, I just don't like them very much. Liquid Tension Experiment, on the other hand, while still not being a whole lot better in the songwriting department, at least doesn't have a singer, which makes them marginally better in my book. (In case you didn't know, although I'm sure you do, LTE is DT minus the bass player and vocalist)