There have been many good articles on this and the debate between 4.10s and 3.73s has in a 4.6ltr GT has been going on for about the last 8 years. If you use the search feature, you'll find many helpful articles.
Here is my input. For an automatic that is n/a, I'de say 4.10 or 4.30 gears. I have 4.30 gears and I like them. It should be noted that if you do not have a transmission cooler for your automatic transmission, I'de get one right away as heat is the number one killer of automatic transmissions and with the new gears, you'll need a cooler to keep the transmission temperatures down. Another neccessity will be either a EEC flash or a sport chip. You will need this to calibrate the speedometer of your car as the automatics are no longer done by a speedometer gear and you will also need it to correct your shift points.
Unless you are going with a power adder, go witht the 4.10's or you will regret it. Trust me, especially with an auto. Which shop did you end up going to for the gears?
You've got to remember the biggest downside: Your going to be revving a lot higher at cruise....IF say you are doing 2k RPM at 60MPH now with stock gears, expect to be around 24-2800 with 4.1;s
The only reason your shop told you to go with 3.73's is so they could get you for another $325 labor(plus a new set of gears) when you come back and have them put in 4.10's when you are dissapointed with them and find out they were wrong in the first place.
Do yourself a favor and use the search option and read ALL THE THREADS about choosing a gear ratio. There are 100's of them I'm sure.
If you get 3.73's for a AUTO you will regret it. If you had a 5spd I wouldn't even care but you have a Auto 4.10's are a must. Don't fear the gear man. Also you will need a programmer or a chip because your shift points and speedo will be all out of wack.