Another vote here for the Never-Dull. Mosin bores aren't chrome plated, but you can make them shine like they are. The Never Dull will even cut cosmoline stains.
For day-to-day cleaning however, I use Ed's Red. It's a home-brew bore cleaner based on the old Frankford Arsenal recipe consisting of equal parts each of:
Sperm whale oil
Turpentine
Acetone
Kerosene
Since sperm whale oil (or any whale oil for that matter) has been banned for use in anything in the U.S. since sometime in the sixties, Dexron III automatic transmission fluid is substituted in it's place. Apparently, in the fifties and early sixties automatic transmission oil was largely whale oil based. The Dexron is a good substitute as it also contains other surfactants that make it useful for use in firearms. If a firearm is being prepared for long-term storage, lanoline can also be added.
I've found that the Ed's Red works great and will not harm metal finishes in any way, cutting through everything but copper fouling; for that I took a tip from an Army technical manual for the 1903 Springfield (TM 9-1270) and I use janitorial strength ammonia (it must be at least 10% ammonium hydroxide), readily available at most hardware stores. Be careful with the ammonia however, as it can stain blued finishes. All that is needed is to moisten a patch and run it through the bore, immediately wiping away any that gets on the outside. Repeat the process until the patch ceases to come out with a green tint.