Hey I might actually be able to add something to this thread. Some background I repair photo machines (among other things) for a living. First off the prints will last longer and be cheaper if you send them out. Now as for quality, it all depends if the guy who is running the machine knows what he is doing, and if he has been staying on top of his chemicals.
First off look at the machine in the behind he counter, if it says Nexlab, or Drylab. It's a big fancy die sub printer, personally I don't get my prints made on these. If the kiosk that you plug your media card into is where they print out, yea it's being made on the same thing you could get at home.
Now if it says something like, AGFA d.Lab 1, Fuji frontier ### (330, 340, 570, etc.) Noristsu QSF, or something like that then it's a real photo machine chemicals and all.
Ok this is company (Walgreens) specific but I would be highly surprised if everyone didn't do these. Ask the guy to show you the "Reference strips" and today's "test strips" he should be able to produce them. The reference strip was run on a known good chemical batch, the test strip should have been run on the machine early that morning. Look at the color of paper and the test boxes, they should be either the same or extremely close. If it's way off then your pics will be off as well (some correction can be made through the caliberations they are suppose to run daily but they will only do so much). Also the calibrations only work on the prints, they do nothing for film. If he said they weren't run yet, or can't produce them I do not get my photo's processed there. This whole thing will probably having him look at you like you are from outer space, but the way I see it is you worked hard on these pictures, they should be done right.
Anyway, sorry for the long winded response, hope this helps someone.
Edited to add:
Be sure you look hard at the yellow test box, it should be a healthy yellow if it looks mustardish then there stabilizer is under powered and you prints wouldn't last overly long. This is important for archival photos