How about instead of a the daily PvP mission, you have two which are exclusive to each other.
One is the PvP, the other a PvE mission.
That way all those that just want to farm emblems can chose what they want to do, but are not forced into a single game style to do so, while allowing both styles to gain the same number of emblems.
Although that's not always the case. I'm sure many are chatting it up with their RP buddies (not knocking RP in general, just as opposed to PVP when in a PVP match), or griping about this that and the other thing being overpowered, or at the very least they could be be downloading porn. At least the porn is understandable.