If you do a search over at AVS, you'll likely come across my one week in home demo of the Studio 40s, Ascend 340SE, and DynAudio 42.
Bottom line, it comes down to what you like. They are very very very differnt sounding, and neither one is necessarily better than the other. I can't stress that enough.
To me, the Paradigm has a very forward, bigger, more room filling sound than the Ascends. They are probably on the brighter side of the specturm, but not necessarily as crisp and clear as the Ascends. Some have said that they sound like a blanket was thrown over them. I found the bass to be plentiful, but lacking punch, but this could be a result of my low end receiver. Although it would seem like I'm down on them, I really enjoyed turning the Paradigms way up and leaning back in my chair and singing along.
The Ascends don't have the forward sound like the Paradigms. I like the forward sound. Many don't. But, the Ascends excel in providing a very accurate sound. If your into critical listening, and want accurate speakers, not ones that emphisis the bass or highs like other brands, then I think the Ascends are the most accurate speaker you can buy for $500 - $800.
Most people who aren't into really listening, prefer the Paradigms upon first listen at my place. But, after a few quick switches and pointing out what to listen for, all would agree that the Ascends were more accurate. After that, it was about 50-50 which was prefered.