Both Es, obviously. One says : If (condition is met), your turn ends (which is after the attack deals damage).

Other E says : If this attack deals damage, (something).

First E was played by the guy that played the attack. Second E is by the one doing the damage.

Which goes through?

In your case if the attack goes through the attacker's effects resolve first. That means it ends the combat phase and straight to the end phase. Floating effects do not continue on through phase changes so the 2nd effect just kinda fizzles.

From V 1.9 Rules

300.1 When a phase or step ends, any effects scheduled to last until the end of that phase or step expire.
300.2 When a phase or step begins, any effects scheduled to last until that phase or step expire.

Stamp for Zero Cross. The active player's effects resolve first.

Note that if the attack was played off turn (EG a reversal) things will work out a bit differently. The turn wouldn't end (since it specifies YOU TURN and it's not your turn to end) but the rest of the effect would go off, though as Tag said the active player's effect "goes off" first.