I have a match coming up that I think will be tight. I believe my opponent has a ohbh. I have played very few matches against ohbh opponents in recent years.
So my question is to those ohbh players out there, what kind of balls do you not like?
Alternatively if you've had success against the ohbh, was there any particular method to the success?
Even when the opponent is really good, hitting high balls with a OHBH is tiring. Very few players are at ease with shoulder-high balls and those who are won't have the muscles to keep doing it for a whole match.
One handed backhands are best suited for fast-paced, low balls games. It's not out of pure luck that it thrived on grass and indoor courts for decades, it was fit for this and exactly this. If you start moving up the contact and force them to generate more pace because the ball is moving more vertically off the bounce, it becomes hard to keep the rhythm for a long time.
However, if you notice that your opponent has great footwork, don't try to pull him off the court on his backhand side. With a one handed backhand, it's a tad easier to hit a big shot while running since you're used to hit with a closed stance... It's also easier to get top spin and angles because of the little extra reach you get with it. So, unless your two hander is good on the run or that your opponent miss hit all of his running backhands, don't play an angle game with your cross-court backhand.
A good play for you, if your backhand is really consistent, would be to act like a pusher, more or less. Force him to hit tons of backhands. At the first occasion, down the line forehand and keep the ball just angled enough with your cross-court backhand so he can't constantly cheat his position to hit inside-out forehands. With time, a one handed backhand player will miss more balls than you, normally.
EDIT
If he's good, he won't hit a backhand off a moonball. He'll run around and hit an inside-out forehand -- and you'll be the one in troubles if it happens. Fortunately, as Fiji might testify, amateurs rarely do have the presence of mind to run around moonballs!