Go with the bow. Less meat damage, quicker kill, easier to trail, same range as a shotgun (with buckshot, not slugs), quieter. It does take some more skill, and hours of practice. If you are unable or unwilling to put the time and effort necessary to become proficient with a compound bow, look into local laws and consider a crossbow. Most areas will let you hunt with a crossbow during gun season, and some even consider it the same as a standard bow. I hunted with one for years, and with a scope, I was confident out to 40 yards.
WylieKy