As a Battle Tower maniac myself, I'd say Duel Screens are far more useful than Detect or Protect.
For example, I use both screens on my lead Yawn Uxie, Reflect aiding Calm Mind Lucario, Light Screen for my Garchomp. With Yawn providing ample time to set up and sweep.
I don't really see what you'll get much out of Protect, UNLESS, you're using a toxic stalling strategy, then it'll be useful. So overall, I'd say it depends overall on what you'd like to accomplish, if you want to be aggressive and set up sweep, screens. If you want to play more of a defensive game, Protect.
When used correctly is iffy, because if the AI starts setting up Double Team, Protect won't save you, while screens can prolong team member survivability and more of a chance to hit. They certainly both have positives and negatives, but I prefer screens.