Both have their pros & cons, there are many happy owners of each brand/model. I could point out some differences but I am not sure they would matter. The only thing I can think of is, if you are the organized plan way in advance type, then the Bradley would be a good purchase for you, however if you run out of pucks because you forgot to order more after the last smoke, type guy, then the MES is a good choice.
I did run out of wood chips one night, no store open. So I just went to my firewood pile, grabbed a piece of almond, chopped up some junks and continued smoking on my MES. That wouldn't happen now, I have a HUGE box of oak sawdust, several different types of pellets, a couple of big bags of chips, and even a bag of chunks. So I can generate smoke with my AMNS or my
AMNPS, or just using the MES chip tray using either chips or chunks, in other words I have a few options for generating smoke. I will tell you that all smoke is NOT equal, some methods as far as I can tell produce a better TBS (thin blue smoke).
You might want to check the bradley size, will it smoke a whole rack of ribs without cutting it? That was important to me when I bought my MES 40, we do a couple big backyard BBQ, and ribs are our traditional meat choice. I can do up to 16 racks of ribs in my MES. If I wanted I could have some special rib standing racks made and do 20 racks. 16 is enough for what we do though. Some have said they don't need that kind of capacity, well if your ribs are any good, your friends will ask if they can bring friend, and those get togethers grow.