transmission ID/problem
 

I've got a 2000 a6, 2.8 Quattro, auto trans, running fine all day, no problems, then 3rd gear started to slip out, then bang back in, changed fluid and filter, didn't help, and now 4th is also doing the same thing, 27 bolt transmission pan, , car has over 150k miles, is it time for a transmission change? or is there something else, no codes have been thrown. if I do need a transmission, I was told there are three models, where exactly do I find the id tag to determine which transmission I have/need to get?