Both are nice guns. My brother has the Baby Eagle in .40, and I have a M&P Pro in 9mm with 5" barrel. The M&P Pro trigger is the best DAO trigger I've encountered. The interchangeable backstraps are nice, letting you choose a grip size that works with your hands. I've also had not one problem with the M&P, no FTF, FTE, stovepipes, or anything else. The BE .40 is also a nice gun, all metal, heavier, but is fun to shoot.
For CC I'd give the nod to the M&P due to weight and magazine capacity.
Tom
Live today, tomorrow may not come!
Boberg XR9S
Kahr CW40
Springfield Armory 1911
Dan Wesson Revolver
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