No it does not. Nobody comes here and say that the P4J demolishes the M4A3 while it naturally wins thanks to its amount of armor. So please refrain yourself from using superlative because the EZ8 wins vs it thanks to its amount of hitpoints.
It has 215 armor, compared to the P4's pen of 125/115/110, of course that plays a big part in the match-up against the P4.
At max range;
Chance for P4J to pen E8: 110/215x100 = 52%
Chance for E8 to pen P4J: 155/234x100 = 66%
At close range:
Chance for P4J to pen E8: 125/215x100 = 58%
Chance for E8 to pen P4J: 200/234x100 = 86%
Theoretical TTK, disregarding accuracy (which is about even, with E8 being 1 target size larger but having better scatter and better moving accuracy),
Time it takes for P4J to kill E8 at max range:
5/(110/215)x5,75 = 56,2 seconds
Time it takes for E8 to kill skirted P4 at max range:
4/(155/234)x6,55 = 39,6 seconds
Time it takes for P4J to kill E8 at near range:
5/(125/215)x5,75 = 49,6 seconds)
Time it takes for E8 to kill P4J at near range:
4/(200/234)x6,55 = 30,5 seconds
So yes it does win, decisively, thanks to its hitpoints
and its relatively high armor (compared to P4 penetration). Especially at close to mid range. An E8 easily wins at range and it demolishes a P4J in a close to mid range brawl.