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Which demon wins?

Abraxis stomps if this is in a neutral setting. In Chthon's dimension it would be closer but Abraxis would still win.

Who won between Abraxis and Spectre?

http://i1149.photobucket.com/albums/o589/lupinw45/AZ_zpssvdwl7fz.jpg

That was a mere aspect of Abraxis who split his consciousness into two dimensions and 5 different time eras. On the other hand it was a time period when Spectre was depowered but still extremely powerful. The Spectre/Abraxis battle happened on only one of those fronts. And they were stalemating till the norse gods empowered JSA overwhelmed Abraxis.

Abraxis had more showings then ARMAGEDDON?

^ Nope. His appearances are limited to that mini/event.

Anyway, Abraxis stomps.