I have a BH and love it! When you have it on your shoulder and your arm is pressed against it, there would be no way for a pickpocket to steal anything from your bag!
I am going to buy the Neverfull MM later today. I like the price ($620) and the fact that there is absolutely no vachetta piping on the bottom of the bag. I also love the interior lining. I think it's very cute how it cinches closed on both sides but the only thing that I wish it had was a cell phone pocket! But, at least there is an inside pocket and d-ring to clip keys.
The BH has the inside pocket, d-ring, and cell phone pocket.
I have the Hampstead MM which is very similar to the Neverfull MM... and even though I think Neverfull MM is also similar to BH, I'm still going to buy it!
The BH is about $100 dollars more than the Neverfull MM..... if you don't care about the price, I'd say go for the BH first. But if you plan to carry alot of stuff, then I think that the Neverfull MM might be good! BH can hold alot of stuff, but the Neverfull MM is huge in comparision to the BH.
Good luck!