I third or fourth the early morning Walks of Italy. I did it in the first week of November. You meet in the same place as other tours, and Walks had enough people that they split everyone up into 2 or 3 seperate groups, each with a guide. They explain the Chapel as you wait in line to get in the museum and while you are practically jogging there with the other morning groups, since they aren't allowed to talk in the chapel, but if you're really interested in detail, I'd recommend reading about it before you go. You walk very quickly to the chapel and get about 20-30 minutes in there. Even though there were other groups, it didn't feel crowded. There was room to move around and plenty of seating on the edges to give you time to really look at the work. I wouldn't go without one of these early tours, and if you get up a little extra early, the nearly empty Piazza San Pietro is a treat.
After the chapel as the regular crowds are let in, you move on to an abbreviated tour of the of the museum. Even in November it's busy, but the tour doesn't feel rushed since you're just hitting the highlights (Laocoon, Rafael rooms, etc.). I might have liked more time with the maps, but otherwise it was good. If there are particular things in the museum you really want to spend time with or see that aren't on the tour (portraits, Egyptian stuff), then the Dark Rome one might be better for you. The only negative with that would be getting from the museum to St. Peters if that's next on your list. You would have to exit the museum, walk all the way around it, and wait in line for St. Peters. With the Walks (and similar) tours, they go back through the Sistine Chapel (where you get to pass through the crowds you missed by going earlier) and take a shortcut to St. Peters. We did a quick walk through the church and made it to the front to see the changing of the guards at 11. The guide pointed out the line to get into St. Peters and said it was about a 2 hour wait. She keep us in the secure area, though, so we could go back inside on our own or go up to the cupola for the view. The guide said there isn't really a downtime for the Vatican.
The point of all this is to say that the morning tours are worth every penny and having to get up early. I'm not sure how the breakfast tours work, but you can always buy something to eat in the hotel and get some espressos after the Vatican. The art will keep you awake.
