What is the finish? Bead blasted, brushed or polished? Some of the methods listed above will affect the finish. With revolvers, I've used them all depending on the situation.
The lead remover cloth can cause shiny spots on a bead blasted finish. Abrasives can scratch a polished finish.
I'm a huge Ballistol fan but I've never had great success with baked on carbon like what is found on the front cylinder face or the corners of the top strap. Maybe I'm not patient enough.
If you're cleaning it up to store it or sell it that's one thing but no need to get the front face of the cylinder spotless every time your shoot.
I've has good success with Slip 2000 Carbon Killer on a crudded up stainless revolver. I applied it where I wanted it and let is stand for awhile then used a combination of paper towels, bronze and nylon brushes. Be sure to read the warnings about what finishes it can negatively affect.
I've been using the lead removal cloth that others have suggested for years. It's the best and fastest way to remove the 'star' splashes of lead that build up on the cylinder face. Do not use this on blued steel. It will remove that too.