Most would say I am biased
First thing - Price difference
The Clarion sells for about 1/2 the Alpine - a bit less if you want iPod control as you need to buy the CCAIPOD cable for the Clarion if you are doing iPod... the Alpine comes with the cable if memory serves..
Clarion is 6V out
Clarion is 2 Year warranty if installed by a dealer
Clarion will play all iPod file types and DRM no issues
Both use 24bit DAC's
Both have Time Alignment
Clarion has AUX input and USB input onboad - extra $$ from Alpine - USB is $259 extra alone
Alpine will have the IMPRINT working next month and I am curious to hear that in a real world car... Could be nice. What is the dealer going to charge you to set it up? It's a $400 retail kit for them to do it from what I understand.. so make sure they are getting that (I can't imagine too many dealers who order the deck not getting it)
On and on for days comparing features I'm sure
There are of course other feature differences... I like the 728 color on the Clarion cause your lighting can be color matched so your dash does not look like a Christmas tree

But those are more personal preferences
For a ~$300 diff - take a look at what you plan on buying next for your system and see if that $300 is going to make a bigger impact there?
IE Going from a Good $500 component set to an awesome $800 will most likely make a more dramatic difference in the SQ, imaging etc of your system
What are you looking for in a deck - especially given the price range diff you are looking at?
What else do you have in your system now, and what are you building towards?