Actually the British "Brown Bess" was a fairly good military weapon of the day. It was much faster at reloading than the American rifle. True the rifle had better range, so much better that the British started hiring Hessians armed with rifles to offset the advantage.
The real reasons that the Patriots won were they were fighting in their own backyards, the approximately 35% that supported the revolution were committed to their beliefs, and most Patriots already knew how to handle firearms. Even so it was close. It almost comes down to the fact that we had George Washington.