I dont know i still dont understand all that stuff -- maybe someone else can help
I would say you will get your bonus. Your "Stop-Ability"-Ability cancels your opponent "Stop-Bonus"-Ability.
The Abilities/Bonus system seems to run on a premise of negations. If you both have a stop bonus or ability both your cards abilites will not work.
Same for Bonus.
It's gets interesting when it gets to -power/attack/damage. but thats another story for the AOD forums.