Dyes do deteriate over time. The same generation of dye can have different batches, where one deteriorates faster than another. If you download a program called CDspeed you can run a Disc Quality test on your burned media. Preferable if you use a Lite-on DVD drive(one of the best readers).
Even though the Xbox360 might be working fine with the games, you might want to run a Disc Quality test on a few of your games every 6 months or so to see how they are holding up. If they are getting pretty bad, then might be time to reburn them.
Verbatim +DL is known to be the best and is the only one that burns pretty good quality DL Movies. I've noticed that DVD Players reading movies tend to be a lot more picky. When the computer is just reading the data then it is fairly fast and there are few problems, generally only when there is a huge scratch or something. I figure the Xbox360 is just reading data off the DVD so it probably isn't as picky as a DVD Player. So most likely you can just go with any DL. Just be sure to check a couple every 6 months to test their deterioration rate.
Edit: Forgot to say that bad media/errors will make your laser work extra hard. PS2s had the problem with dying lasers, and if you used a lot of crappy media you could end up killing your laser prematurely.