Kotor or Mostar & Kravica
 

Only know Mostar and that's a great and informative trip. It's been a while but I had a tour of the town given by a former exile who knew the war very intimately (sadly, far too intimately). She was around 18 years old. Riveting. Since that 10-12 years ago I'm sure things have "softened" but you get the idea that there is unfinished business among many.

Keep in mind that this is an extremely popular day trip from all over the region. Not necessarily a big negative as long as you have the right expectation.

I have been to both, enjoyed both. But, I would give the edge to Mostar as it held my attention more. I too took a tour given by a native while there. The history during the war was interesting as was the combination of both Muslim and Christian cultures. Mostar will be more of a contrast to Dubrovnik. Kotor was lovely but limited in sights. I have also heard that it is now inundated by cruise ship passengers. Plus, it is more like Dubrovnik in setting and appearance. For a different experience, I would choose Mostar. BTW, there are lots of tour companies offering day trips to Mostar. I found taking a local bus to/from easy and interesting. I had prearranged a tour with a local before going.

If you just go to Mostar just to visit the Old Town, you'll find that the area is mobbed between 1000-1600 with day trippers.

At least a Guided Tour will provide you with some of the bloody recent history.

In the Old Town be careful underfoot, loads of cobbles, and crossing the Bridge can be tricky too if you've got any mobility issues.

Far better to at least include an overnight stay, with perhaps a trip to Medjugorje, a Roman Catholic Pilgrimage Site. No need to be RC to enjoy the vibe, and the scenery on the ride up into the hills is very pretty.