When most of us think squirrel hunting we think .22 rifles. How many gun articles have you seen titled "squirrel shotguns" Being said, I use both for no other reason than I can. Squirrel can be a lot tougher than people give them credit for. Even with 12ga #6 pheasant loads many shot will be right under the skin and if you use the right choke and don't shoot em close up you won't blow em up. Cottontails are a different story. Most fall over if you look at em cross eyed and ranges can be remarkably short. Sometimes measured in feet instead of yards. Open choke with small shot works great. To use the same shotgun on both you have to go with a compromise. #6 with an improved choke?
.410 sucks. Yuck, Yuck, Yuck. Glad I got that off my chest.
Take what you want, live with your choice.
LK