How do the PvE prizes have any effect on the PvP prizes?
I don't see how giving the same prize is a problem, at all. Aren't these gift Pokemon we're talking about? Who cares.
Give the PvE people the same prizes. Literally no reason not to--besides selfish PvP players feeling entitled to better things than people who don't play PvP, which is ridiculous.
If you have a problem with fair PvE prizes and you play PvP, enter the PvE events and win yourself.