I usually use a scope. However my last buck and my last few hunting trips have been with open sights. The potential shots from my blind are short. I have been using my BK92 and as a plunger gun, it is much easier to clean and prime without a scope. My Disc Elite remains scoped; especially since it does not have open sights!
I think the biggest advantage for a scope is that it is faster than open sights. You can aquire the target more quickly and you don't have to take as much time to "think" about proper aiming technique.
Now for a little bit of controversy. Under proper conditions, and with proper technique, a peep sight system can be just as accurate as a scope. Now before everyone screams, proper conditions almost always mean at the range with a target big enough to see the outline outside of what the front post covers. Those of you who were in the Marine Corps know what I am saying. On the "known distance rifle qualification course" (KD course) we were required to shoot at 500 meters with an M16. The target were 6' by 6' at the frame with the paper bullseye in the exact middle of the target board. Of course we shot from the prone position at that range. We used a tight sling hold. Many of my fellow Marines and I could hold 10 rounds in the 10" bull each time on light wind days. Not everyone could do this, but most who qualified Expert could. Now this type of shooting is nearly useless for hunting. I see the videos of guy using 20x scopes mounted on their 300 Ohmygosh Hoochy Wizbang Magnums take elk at 1000+ yards. The elk are always stationary and the shooter has time to set up on a bipod and execute perfect target shooting form. Nice for video, fun for shooter, not much real world hunting involved.
Also, I recently read an article by Mike Venturino espousing this same point that I had know for years. He pointed out that in the last BP Cartridge Shilouette championship the winning scores for the open sight division were virtually identical to the scoped division. Again thought, this competition is fired under ideal range conditions and not hunting conditions.