A bore snake is useful for removing combustion products, but has little effect on lead or bronze residues. On the other hand, metal streaks are hard to remove by any method, including solvent and patches.
The advantage of a bore snake is that you can clean from the receiver rather than the muzzle, often without disassembly. Most bore damage can be attributed to muzzle wear, which is much less likely to occur by using a bore snake. It's by far the best option when cleaning a revolver, semi-automatic rifles and most lever guns.
When I want to clean down to the steel, I use J-B Bore Cleaner and Bore Polish. It takes two applications, using about 30 strokes each, to remove all lead and bronze - anything softer than steel. I use bore guides, especially when cleaning from the muzzle. They're cheap and effective insurance.
When the bore snake gets dirty, put it in a lingerie bag and run it through the washing machine. Don't run it with other laundry, and never put it in a dish washer (Lead poisoning! We have enough people voting Democratic as it is.)