I have three different pairs of compression shorts from Shockdoctor.
I bought the standard pair a couple of years ago, and did have some trouble with the cup slipping around. I always wear briefs under though.
I then bought the Double compression shorts, and still used the regular cup. Had less trouble and was satisfied.
Then a couple of months ago I bought the ultra compression shorts with the bioflex cup. It was a little different. Kind of like a jock inside of compression shorts. It worked the best, but due to the bioflex cup, I can use all the other shorts without issues.