I have lived overseas for nine years, including four in Germany. Also, since retired visited 78 foreign countries. We have been all over Germany and the UK as well as Italy, France, Spain, Portugal, etc.
I agree that places like Rothenberg ob der Tauber, Brugges, the Cotswolds are usually jammed with tourists.
Also, there are other places similar to Rothenberg, for example on the Romantic Road, there is Dinkelsbuhl, which is a preserved medieval city. There are other such cites in Germany. Some of my favorites are Trier, Heidelberg, Augsburg, Bamberg, Regensberg, Triberg and Strasbourg, France (across the river from Germany).
However, I found Rothenberg to be special and would advise anyone that hasn't been there to visit that city, as well as take the Romantic Road.
As for the Cotswolds, we loved it there and based there for six nights to visit Oxford, Blenheim Palace, Stratford Upon Avon and of course the several villages, towns and small cites of the Cotswolds. True, there are other great places to visit in the UK, we especially loved York/Durham and Winchester/Salisbury. Also, the Lake District is nice for nature. Tenby, Wales is special and I don't have room for details on Scotland. Still, I would say the same, if you haven't been there, go, but don't miss out on other great places.