Many would like to play non-boosted and put up with the speed ties. Others like their heavily boosted teams and would rather play boosted. Some may be willing to do both.
My suggestion is to add a PvP setting that give each player 3 choices of play.
1 - Play boosted only
2 - Play either with or without boosts
3 - Play without boosts only
The settings will give a warning that playing only with or only without boosts may make it take longer to find matches.
Then when we go into PvP it will search for an opponent that matches our choice. There would be no need for a separate arena.
Playing Boosted Only
You would be matched with others who either only want to play boosted or those willing to play either with or without boosts.
Playing With or Without Boosts
This choice will have you matched with anyone and everyone. You may play boosted in one match and non-boosted in the next.
Playing Non-boosted Only
You would be matched with others who only want to play without boosts or those willing to play either with or without boosts.
When Entering PvP and you get the battle screen, you will also have a message on the screen somewhere that says “Boosted Play” or “Non-Boosted Play” which would be more for those who are playing both so they know their heavily speeded creatures may not have that 1st attack advantage or that extra attack power.
It would probably be too much to have a boosted and non-boosted arena trophy score. In essence you would end up playing in two different arena backdrops. Some may get farther playing without boosts than with boosts.
Personally, I would prefer non-boosted skilled PvP play. That is pretty much what I play now. I would definitely be much farther if I wasn’t always trying to out skill boosted teams with non-boosted creatures.