My personal experience, and my main reason for using musket caps, is that just like the posters above, I find them easier to handle. It's not a major issue on the range, but when I climb into a deer stand in the dark and it's 20 degrees, I'd rather not have to fiddle with a #11.
Anecdotally, though, I'll offer this story: I was hunting with my brother in law a few years back. I had my normal hunting rifle (TC with musket caps and real powder), and he had a TC with the #11 cap and Pyrodex. Our stands were a couple hundred yards apart. A little after sunrise I heard two caps pop. He was sighted in on a buck and had a misfire, then recapped and had a second misfire before the buck stared at him and walked off. I suspect that he didn't heed my advice and left a little oil in the breech area when he cleaned the rifle last. He popped two more caps trying to unload it with no success. I swapped my nipple into his rifle and the first musket cap sent it downrange. That's not a scientific test, and it's very possible that the next #11 could have done the same, but it sold me on musket caps for hunting. I feel like it's a little extra insurance in adverse conditions. Plus they're easier to handle and I bought a case of them.