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yes, you can use a diff from a six speed. 3.42s would be an upgrade for you, but I often hear the A4 guys suggesting to go to 3.73s if you are going to the trouble, and get a good stall to match it up.
You will need your shift points readjusted after the swap, so if you are not so equipped to program, have someone or something standing by to do that for you.
And I wouldn't put a 3.42 or better gear into a series 1 carrier (which yours should be, I believe), gette a 6speed stocker series 2, or better yet the LS6 series 3 carrier. There was someone selling one in the C5 parts for $750, good deal too, probably gone though!
Wow I don't have an auto, but converting from a 3.15 to a 3.73 should really make a drastic Improvement! Even the 3.42's would make a big difference, my friend went to the 3.42 and he said the difference Is like night & day.... He orig. had the 2.73's though. Good luck & enjoy your new found power!!