I think both makes stamina drop a bit faster if you use it often, but I'm sure run and gun makes stamina drop. my 26 year old SG stamina dropped after 3 games in a row of run and gun (i was new at the time). Yeah but I think Base Offense is the normal speed, and Patient slows down stamina loss.
Run 'n Gun has absolutely no effect on making your players stamina drop. Players Stamina always goes down a very little amount every week, it has nothing to do with what tactics you play.
I've learn in my two full seasons here, it's not so much about tactics, but knowing your players and playing tactics that goes along with their strengths...the less you worry about the other team, and more about your team...the better of you are. This season, I rarely scout my opponents.