Are you making a cake, or what we call here in my neck of the woods, bars? It shouldn't make much difference with bars, if you go with a bigger pan they'll just be a bit thinner. You may need to increase or decrease the baking time depending on the pan size.
She who dies with the most toys, wins.
I'd use the 9X9 - that's close enough in size that it won't make much of a difference. Your dessert would end up being too thin in a 13X9.
9 x 9 is 81 sq inches. Your squares would be 20% thicker. 13 x 9 is 117 sq inches. Your squares would be 20% thinner. Depending on the recipe, either would work. The cooking times would be different. I'd use the tried and true stick a toothpick in it test for doneness.