I own both. The M&P is ambi, the Sigma is not. So in that respect, they are nothing alike. Both have good ergos. The Sigma is a bit heavier. I've had feed problems with WWB in the Sigma (thoughfew, and I may have been limp wristing), and I've only ever had feed problems with a few handloads in the M&P. The M&P is 1 inch longer total length, but only 1/4" longer from slide front to back. The M&P is also longer in the grip. The slide serations on the M&P give you a better grip.
I'm not sure how you could equate two guns from the same manufacturer, with different designs as being the same except the trigger. If you're asking whether you should buy one or the other, I'd recommend an M&P. As to smithing the Sigma trigger, it's not worth the effort. You'll only be able to get it down to where the M&P factory triggers are by sacrificing safety. The Sigma trigger was designed to avoid AD while conceal carrying, and to meet every states' requirements to sell them there. If you're looking at an inexpensive carry piece or are transitioning from wheel guns to autos, the Sigma is perfectly fine and the latest models have been performing almost flawlessly.