Sarlat or Limoges

Sarlat, for sure. Be sure you have a car to visit the many sights in the Dordogne. I would allocate all my time to that area (not just in Sarlat).

Sarlat. But don't stay there. Get a car and stay in whatever excellent accommodation you find in that area. You don't say when you're going, but if it's this year, be sure to drive through Abjat-sur-Bandiat to see if the (synthetic) flower garlands are still up from the Felibree, which was about a month ago. If it's next year after, the festival will be in Brantome the first weekend in July.

I have never been to either. But Limoges in 'on my list" as it is the closest major town accessible by mass transit from elsewhere in France to Oradour-sur-Glane. Oradour-sur-Glane is the town effectively wiped out—along with all of her inhabitants—by the Nazis shortly after D-day. It was subsequently memorialized and kept in its preserved, ruined state by President De Gaulle to forever remind people of these atrocities. If for no other reason, this would be my choice. I hope to get there someday in the next couple of years.

Oradour-sur-Glane is very moving.
Well worth a visit.
We visited. Highly recommended.

For what it's worth, in 2009 we stayed for a few days in the Dordogne area at a chateau hotel (must have changed the name, my notes say La Fleurie but I couldn't find it) and loved it. Much cheaper than staying at a chateau hotel in the Loire Valley. Enjoyed Sarlat market, the prehistoric caves, boat ride on the Dordogne, river towns, Castelnaud (great medieval castle), driving around the countryside, etc. A car is necessary for this area and parking was not a problem.
We also stopped at Oradour-Sur-Glane, very sobering, not to be missed if possible.
-Bruce

Thanks all! I am going to keep 3 nights in each.

I would split 4-2 : 4 nights in Sarlat, 2 in Limoges. You don't need much more than half a day in Limoges itself, and the main day trip is Oradour sur Glane. Conversely, 3 nights feels too short for Périgord.

We really liked Sarlat as a base to visit prehistoric caves and museums. Not a lot in the town, but some decent places to eat. Mostly non-American tourists, seemingly Spanish and Portuguese and a few from UK. Amboise was also nice, castles and chateaus. Better food choices than Sarlat in my opinion.

The drive from Aix up through Carcasson, Albi, Cahors, to Sarlet was a great slice of rural France most do not see.

We drove to Oradour from near Sarlat, (Domme) on a day trip. I thought it was among the most moving sights in France, if not all of Europe.