I went to Carlsbad Caverns a few days ago and brought the 6D with me. I didn't want to bring a tripod, and I didn't want to use flash....so all is handheld in a pretty dim location. Very few throwaways (for focus/blur reason...well, some had a little blur, but usable for smaller prints ). I also had very very little problem with locking focus even in very dim areas. The exception was when it was both very dim, and very low contrast. I did have to shoot mostly at ISO 4000/8000, so noise was a contender. Shot at -1EV to bring up the shutter speed a tad. Not sure if it was a good idea or not (I'm a fair noobie compared to most).
6D, 24-105L @ 24 mm, 1/8sec, f/4.0, iso 4000
6D, 24-105L@65 mm, 1/40sec, f/4.0, iso 2000
6D, 24-105L @ 47 mm, 1/25sec, f/4.0, iso 8000