Both work just fine. If you have heavy copper fouling one of the ammonia based cleaners works faster, Hoppe's calls their's Benchrest. Picking cleaning supplies is more of a preference than something that can be absolutely proved better or worse. The Foulout systems may be the one exception, but you still need standard solvents etc to remove the powder fouling and expose the bare metals for the electrolytic action to work on the lead and copper. The biggest advantage of the Foulout systems isn't the cleaning action, it's that they can reliably tell you when your barrel actually is completely clean of metal fouling without examining it with a high-priced bore-scope.
Except for artic cold conditions, where you need a dry lubricant that won't freeze solid like grease or oils, lubrication is also pretty much a matter of preference & opinion. Dry lubes may attract less fouling than oil or grease, greases may stay put better than oils, and gum up faster with fouling or cold.
There are recipes for home-made cleaners (Ed's Red I think is the most well known); or you can buy the commercial cleaner of your choice for whatever price you are comfortable with; and use the lubricant you believe in and like the most. It's more a matter of preference on how you want to care for your guns than a matter of something NOT working.