That's a nice dilemma, as both are good destinations.
Lyon is something of a foodie destination, regarded by many as the culinary capital of France. Good mix of stuff to entertain the visitor: Roman remains, cathedral, old town full of character, good art gallery, reasonable shopping.
Bordeaux is smaller. Also a good food destination, plenty of fine buildings (another cathedral, of course), superb museum, very good shopping. Visit to Sarlat by train a good idea (nice rail trip, very appealing town).
Both are, unsurprisingly, good for wine, and both have good public transport that is easy to figure out. Both cities have appealing riversides.
Right now, I'd possibly favour Lyon. But ask me tomorrow, and I might vote for Bordeaux.