Do you prefer Deep Purple, or Dream Theater?  

For me, its simply Deep Purple, for a number of reasons. They are, Ritchie Blackmore, Ian Gillan, Roger Glover, Ian Paice, Jon Lord and David Coverdale.

I prefer Dream Theater, is my type of music I like more.
But... I can't deny that Deep Purple is a great band! One of the greatest band ever.
No matter if is Coverdale or Gillian singin', DP are a such a great band!
One of the most influent rock band ever.

definetly Dream Theater.
in my opinion they have so much more than what Deep Purple has in their music.
besides the compositions that dream theater make, they also do some crazy cool stuff, like encrypting symbolic thing into their songs, (for example: the album and the song Octavarium. )
they also connect their albums together with a story like in Scenes of a memory (metropolis).
anyways deep purple is very good, but they are not as special as Dream Theater, not to mention that each of dream theater's player is a legend.

I'll take classic Ian Gillian-era Deep Purple. The song writing complemented his vocals in an exciting manner. Dream Theater has too much technical over-indulgence in their songs to be truly great, though they can be interesting at times.