Of the two you've asked about, I know and own the M&P45c. I also own two Glocks but not the model you've asked about (the G20 and G29). Happy to say I absolutely love the 1911 (and own one), and 5 years ago was a full up 1911 bigot. It's still to this day, IMO, an extraordinary firearm. I carry the MP45c, and have to say it is the handgun I shoot more accurately and confidently than any handgun I've ever handled. I found the trigger out of the box to be pretty much 'nasty', but that's true with many handguns these days and IMO Glock is certainly the apex of crap triggers. The M&P triggers aren't great, either. But, super easy to fix, and relatively cheap to replace with better feeling triggers.
I'm able to shoot my M&P45c faster and more accurately than any other handgun I've fired, as well, and it's comfortable to hold and to carry. I've also owned a Sig P220, and absolutely love shooting the P229, so I'm not biased against the Sig option. Sometimes you really have to shoot them to know them...but I have to say a plastic pistol was out of the question when I range tested about 5 handguns, including an HK, a Glock, a Sig compact and the M&P. For me, the M&P was the no-contest winner of the bunch, and 5 years later I feel the same way.
Your choice would ideally come from a similar 'no contest' experience after shooting what's available. Hopefully, something would really stand out for you. For me, Glock and HK 'really stood out', but at the bottom of the heap.
I also carry the G29, and must say I love it, despite it feeling a bit like a brick compared to an actual handgun made for a human. But, it's 10mm, it shoots well, and it carries well. So, I find it an exceptional carry gun and have pumped probably 5,000 rds through it now so it doesn't feel so weird anymore.
But in 45, the M&P45 compact is, for me, the most ideal size there is for a 45 carry. I highly recommend a look-see. Naturally, if it's just a range toy and carry isn't a concern, you've got a lot of options where size and weight may not be big concerns.