Knots used to join ropes for rappel can be classified according to three main criteria:
1. Do the tails leave the knot from the same side (e.g., overhand) or opposite sides (e.g., fisherman's)?
2. Are the strands wrapped individually (e.g., fisherman's) or together (e.g., overhand)?
3. How many wraps? (The overhand has one and the double fisherman has two.)
My favorite knot to join rappel ropes is such that:
1. The tails exit from the same side of the knot. Smaller chance that it gets caught.
2. The strands are wrapped together. Nice, tight package, though it takes a bit more practice to learn.
3. Two wraps. Does not roll and works for ropes of different diameter too.
I posted pictures here on SP several years ago. I believe they are still there.
The other common knots correspond to other combinations and they may have some pros and cons. The simple overhand is... simple, fast to tie, easy to inspect, not bulky, the one with the least chance of getting caught. It's a one-wrap knot, which makes it more prone to rolling than the two-wrap (or three-wrap) knots. The knot proposed by Bachmann is like a double fisherman's (two wraps, strands wrapped individually,) but with the tails leaving from the same side. For rappelling, I see no reason besides habit not to prefer it to the double fisherman's. The overhand with a second, backup knot is classified just like mine, though it is a bit different. It's very easy to learn, though not as neat. Finally, the figure-eight knot is not for joining rappel ropes because it is inferior to the overhand for that application.
