Since Vermintide is heavily inspired from the core gameplay of Left4Dead, perhaps taking a cue from L4D2 could be useful.
In L4D2 PvP was handled by a 4v4 indirect game mode.
The mode was played in 2 rounds with the goal of one team playing the role of the heroes challenged with a task, usually fetching a number of gas cans scattered throughout the level and bringing them back to fill up a generator or the escape car to complete the task.
Team 1 would play first and basically set the time which Team 2 would then have to beat. Team 2 would play on the side of the horde, taking control of a Special enemy that would spawn in on a delay. There were rules for when, where and how often a member of Team 2 was allowed to spawn in.
When Team 1 completed the task, the entire group was wiped out, or the maximum allotted time for the task expired, the roles of each Team switched places. Now Team 2 would play the heroes and the outcome of the previous round would be the timed goal Team 2 would have to beat.
In this way, neither team directly competes against the other. They indirectly compete by setting a challenge their opponents would have to best. For example, if Team 1 finished the round in 5 minutes, then Team 2 would have to complete the same task in less than 5 minutes. Whatever team is not playing the Heroes, they control regular enemy special and eilte types and are simply trying to slow down and distract the current hero team as much as possible.
Vermintide 2 would have to expand the idea to accommodate its unique take on L4D mechanics, but there wouldn’t be normally expected balancing pitfalls of trying to pit PvE character abilities and gear directly against other Players using the same.