Is cordless Air nailer as good as corded Air nailer in terms of power?
I want to buy a finish Air Nailer but I hate the one with the compressor but I was wondering if the cordless is just as good as the corded.I really don't care about the accessibility just power I'm concern about.

Really depends on the tool purpose.
If you are doing your own house and occasional work, cordless should be fine, if this is your livelyhood.....
as far as power, think of cordless drills.
Bigger the battery, more power,more weight.

I haven't heard many complaints about the cordless models that use the charge packs. The cost is higher for the packs but if you don't want to have a compressor or listen to it you'll be ok with one, I think it is Paslode Impulse or something like that.

I have never seen a battery powered nailer like what you're talking. I think previous message was in reference driver drills and other tools that are now commonly battery powered.