Closest you'll get to a BGE would be an insulated cabinet smoker. With or without a water pan. There's a ton of really good ones out there. I'm a Spicewine fan, mainly because they're local to me and I like to support my hometown peeps. But a Stumps, Backwoods, Vault or any other insulated cabinet smoker would likely do just as well. Add a Guru or similar computer-aided draft device and you really end up with a smokey crock pot. Truly set and forget.
Stick burners just require a lot more attention and interaction. They have a lot more hot and cold spots so you need to maneuver your product a lot more to get even cooking, but you also get the benefit of multiple cooking temps in one cooker and usually more grillestate.
Pro Q Frontier, UDS (Little Red), "Turtle Drum" UDS, CG Gasser KCBS CBJ#61160