Advantage BP -- same batteries (though TR001 charger can be used with both battery types). Advantage IP -- slimmer, more "refined" look; price (though a new IP with new IP batts will be about the same $ as a bare additional BP). Wash -- run time (Infinity batts are true 650 mAh, same as the Powerizer batts for BP), operating characteristics (same voltage range, current,...).
A tough decision

I like both my original Infinity and the new BP a lot, don't use any other PVs.