They shouldn't! They are NOT equal. Also...Colosseum ultimate hi is 12 gems, while it is 30 on the arena. So you would lose more than 2 as many gems to "keep the streak". Also...I have finished the colosseum - currently - if I don't touch it - my HUGE streak should stay and remain until the next battle starts there- all the bonuses intact and ready to go. But now - Although I have already won the Automath - if I lose even one battle on arena - I would lose all that! Those are separate buildings and players should NOT worry about losing their streak while they are doing normal tournament on arena or battlegrounds!