I already made some comparisons earlier in the thread. Are there any other things you would like me to cover?
The Alpha dogs sound quicker, more accurate, and the bass has more definition and rumble when the recording calls for it.
The Paradox is recessed in the 3KHz region (upper mids). Alpha Dogs has some upper mids emphasis (more upper mids than what I believe is neutral). The Alpha Dogs has improved bass texture. The Alpha Dogs seem slightly recessed at 10KHz. The Paradox has more 10KHz emphasis.
Take this with a grain of salt but from memory I think the Paradox has better soundstage than the Alpha Dogs. I was pretty satisfied with the Paradox soundstage when I owned it, unlike my disatisfacation of the Alpha Dogs soundstage right now.