I have hunted alot with both, and I much prefer the ADL. I don't like the hollow "clunk" sound the BDL makes when when you set it down on something. I hate coming back from a hunt in cold weather, and taking off my gloves and trying to find the release button of the floor plate with numb fingers and fumbling with the swinging floor plate, and then trying fit the floorplate and spring back up into the magazine well before trying to snap the floor plate back in place.
The ADL is much faster to unload than the BDL. Just kneel down on one knee, point the muzzle towards the ground, and cycle the bolt 7 times. You are done. All of the shells fall in one neat pile.
The ADL is just a no muss, no fuss, no problem design.