I'd offer that neither is what I'd consider a 'bad' choice.
I own a late-production 3913. It's always been my 'favorite' 9mm compact. Fairly lightweight, nicely balanced, reliable, as inherently accurate as you could ask from a compact pistol ... and I happen to like traditional double action triggers for working guns. It fills the hand and has a bit more heft toward the muzzle than my CS9.
Interestingly enough, my SW99 (TDA trigger) 9mm compact actually has a bit better trigger, and I can actually wring just a bit better practical accuracy out of it than I can my 3913 at longer ranges ... but I prefer the handling characteristics of the 3913 for rapid shot strings. The 3913 snaps back onto target with a bit more certainty than the SW99. Not sure why, but it could just be the combination of its ergonomics, overall weight & balance and my shooting grip.
I carry the 3913 more than the SW99, though. Splitting hairs when it comes to inherent accuracy at 25-35 yards ... especially when both pistols can do very well at those distances for me ... isn't enough reason for me to discard the perceived advantages I experience when it comes to balance, recoil recovery and controllability with the fast-handling 3913 at reasonable handgun ranges (1-11+ yds).
Now, the M&P pistol? Nice little gun. I ordered a compact chambered in .40 S&W instead of 9mm, though. I felt I was well enough covered in 9mm with my 3913, CS9, SW99 and G26. They give me enough choices which suit my needs.
I felt like I wanted something else in the .40 S&W category, though. While I feel my G27, 4040PD and 4013TSW are very good quality examples of small pistols chambered in that caliber, they all seemed to lack something I thought I'd like to have for a long term off-duty/retirement CCW gun in that caliber. It's not like I haven't had sufficient time with all of them to consider their relative merits, either. I have more than 9K through the G27, over 1K through the 4040PD and a few thousand through the 4013TSW (and I carried an issued one for a while, too).
I'm thinking the M&P 40c may fill that niche in my working collection. I'll know better once I have some range sessions and qualification runs under my belt.
If you're going to experience humidity and sweat, and you decide on the 908 over the M&P, I'd opt for a 908S (stainless) version.
The plastic guide rod can be replaced with the standard metal one used in the 3913/3913TSW.
Matter of fact, if the presence of the light rail doesn't bother you, the 3913TSW might be an even better choice than the standard 908S, although they take different leather because of the rail. I've always had picking up a 3913TSW to compliment my 3913 in the back of my mind.
The TSW has the box-type frame and slide rails, which can lend to slightly better inherent potential accuracy. Tighter tolerances, but not so tight that it adversely affects functioning and reliability. The TSW barrel profile allows for delayed unlocking, which can reduce the feel of recoil (although we're only talking about 9mm, after all). The loaded chamber visual inspection port located in the rear of the barrel tab is a handy thing, too, permitting the user to see the case rim of a chambered round.
The slim grip of the 3913/908 is nice, although the checkered Delrin grips may be considered a bit slippery for some folks. The excellent Hogue soft rubber grips panels are a nice option, making the 9mm pistols even more controllable, although they can snag on cover clothing. Take your choice of advantages/disadvantages.
This is where the M&P's replaceable grip inserts are a nice touch. They not only change the profile of the rear of the grip strap, but they offer some palm swell difference, as well.
The newer production M&P compact 9/40/357 models are going to be offered with thumb safeties, if that's something that interests you. While I ordered the M&P 45 Dark Earth w/thumb safeties, I did so because I own a handful of 1911's and have spent a fair amount of time acquiring the manipulative skill to use a Colt style safety lock/thumb safety. When I ordered my M&P 40c, however, I went for the standard version without thumb safeties.
I've already stated in some other threads how well I like the M&P design ... and why ... and how well I've come to like and trust the S&W TDA design over many years of carrying one on-duty, for that matter.
As an armorer I respect a number of pistol platforms, including both the S&W TDA and the M&P.
Choose whichever better suits your anticipated needs and desires. Do you have any experience with either, such as on a rental range? Might help you with your decision.
Not everyone likes TDA pistols, and not everyone likes the various designs found among the various striker-fired pistols. Personal experience and preference might push you toward one or the other ... and some hands-on experience with both might be helpful.
Just my thoughts.
Luck to you.
Best regards.