I personally like the alpine, because its a mono amp so its designed for your subs. It all depends what you want to power the subs alone or maybe subs/speakers.
If your running subs, then yes go with the mono, compared to those choices you listed,(The P4004 is not that great in my experience). I have that alpine amp and I am very happy with it , but its not the greatest if you have hungry subs. What kind of subs you have?
Yes, the kicker would be slightly better. I like your subs , I use to have 3 of them and was very impressed. Anyways I'm assuming you have the new type S, it will do the job but you may want to get a more powerful amp or maybe 2 of either the alpine or kicker for each sub.