Avignon : Much smaller city some much more quiet and peacefull but also with much more interesting for tourism since, from 1309 to 1423, the popes lived not in the Vatican but in Avignon so you gotta visit the Palais des Papes (Popes' Palace).
Bordeaux : Bigger city but still quite peaceful. It has some nice places to see and visit but nothing as important as the Palais des Papes. It also has the Atlantic but in ocean and the beach. But most likely the beach will be crowded...
And it has much more wines.
In fact, if you're planning for 2-3 vdays, I'd say Avignon would be better but if yo're planning for more Bordeaux would be a wiser choice.