I haven't seen either car but 117,000 miles is getting up into the expensive scheduled maintenance territory. It's also about 20,000 miles a year. The Camry is older but has been driven only 6700 miles a year. I expect that the Camry is also less expensive to operate and repair. The Avalons are nice but the mileage and dollars are too high. If the Camry craps out, well then you "only" spent 8950.
I "might" give them 7k out the door on the camry but that is it. The car is 11 years old regardless of the miles. They probably only allowed 5k or so on the trade in if that. According to NADA clean trade in only $5400 and I would be surprised if they gave that.
If it is still there in a few days and I don't find something else I may go back and make that offer. Right now I am just going to set back and see what privately owned vehicles come up and drive my junk unless I am forced to make a different play.
All that said the Camry drove great.