underpowered sub

Hmm.  That might depend more on you than anything else.  The sub with the 1000w power rating probably sounds better at output, and probably has a lower sensitivity than the 500w sub.  However, as you say, you're only gonna run 400w to it.  If you like SQ more, I'd go with the 1000w sub.  If you want output, go with the 500w sub.

If you tell me what kinda of subs they are, and link to a pdf or a manufacturer's spec page with the t/s parameters, I'll model them in WinISD and answer your question definitively.

I think heamph thought you were talking about a 1000watt amp vs. a 400watt amp.

Anyway.. wow I can't find t/s parameters for that Alpine sub ... the Alpine website doesn't even link to a pdf or anything off the product page.   ...so there really isn't anyway for me to compare them.  What kinda enclosure do you plan on using? 

Just looking at the Pioneer tho, I'm not very impressed.  Any sub rated at 1000w with all of 11mm of excursion tells me this thing probably isn't a 1000w sub.  For about that amount of money have you considered a JLw3?  The pound is *really* strong right now American imports can't be that expensive..

I dunno man.  Anyway, like heamph said, there really isn't a such thing as 'underpowering' a sub.  The RMS power ratings are thermal guidelines.. the actual power applied needn't be what the sub is rated at.  You might be best off getting whichever is cheaper.

Looks like Alpine has changed their website to a less friendly format.  I did at one time, however, get the parameters for this sub from the site and have them in my WinISD database.  Here is what it looks like:  swr1222ddatabase.jpg

Note that this sub is a DVC 2 ohm model.  It will wire to 4 ohms (or 1 ohm).

These are default alignments in WinISD Pro.  Only change I made was vent diameter to 4" instead of 4.02, and gave 400 watts as power input.  Blue is (Super-) Boom-box and green is (Sub-) Chebyshev:

alpinjeswr1222daligns.jpg

And this is cone excursion for these alignments:  alpinjeswr1222dexcursion.jpg

i had a couple pairs of those pioneers.  i loved how they sounded.  they hit real LOW.  at least, in a sealed 1.25 cu ft box (lined with fiberglass for strength, and a little polyfill in the box).  but, i was a little disappointed that they couldn't seem to handle rated power.  :(    I blew up three pairs in two months- I haven't blown a sub in almost 10 years!) If i was running a smaller amp like you are, they should be fine. 

also, i did try it in a ported box.  it seemed to handle more power, and definitely hit better spl.  but it only hit certain notes  (real hard!)...gave me a headache so i went back to sealed box