Although, if the opponent is also strong, I would let that affect their chance to be intimidated. I don't see the Str 20 dude using strength to intimidate the Str 30 dude.
That's why we have opposed skill checks!
After all, I'm sure that, like me, you know someone who refuses to be intimidated...
A buddy of mine once charged an entire football team to figure out which one of the dudes called him by a racial slur.
He was 5'6" 125lbs.