If you do the Romantic Road, you actually enter Bavaria almost immediately as you head east from Frankfurt - Bavaria starts just after Hanau.
You don't say how much time you have, an important factor.
You're decision will be made by comparing apples to oranges - it depends a lot on your preferences.
If you choose the Black Forest, that means you're more probably more interested in outdoor activities - maybe some hiking, mountainbiking, that sort of thing. There are lots of mountains, some dramatic train rides, several attractive half-timbered towns. I spent close to a week there this past June and had a wonderful time, but I wasn't looking for history, art, or that sort of thing on this trip.
If you choose the Romantic Road, you're probably looking for old world towns and a cities, historical sites, and a lot more international tourism. Würzburg and Rothenburg are really worthwhile, and many of the other towns are too. The RR itself provides pleasant scenery, but nothing any more noteworthy than the rest of Bavaria. I would encourage you to avoid sticking only to the RR, which can become an unromantic parking lot because for some reason, people think it's only the RR towns that are worth visiting. In fact, Nuremberg, Bamberg, Weissenburg, Eichstaett, and several other non-RR towns are more visit-worthy than the average RR town and less overrun with tourism.
I would caution you that you should avoid Munich during Oktoberfest if you don't plan to make an event of it - it's a very crowded and expensive time to be there.