In a 2" barrel revolver, the issue is not going to really be the velocity of the bullet --the 357 Magnum will out perform the 38 Special, period. The issue, as ArmedBear says, is going to be the weight--and probably the perceived recoil.
With a 158-gr. bullet, about the maximum performance I can wring out of a 38+P handloaded to maximum specs (CIP, not 38+P) in my 640 is about 850-870 fps; with a 357 case loaded to maximum with silhouette, that went about 1110-1150 fps.
A 640 weighs 23 oz. empty. I found the max-power 357 round to be shootable with a properly condiioned hand, including at a measured-rapid-fire rate (about 1 rd per second), and coming back to target.
An M&P340 weighs 13.3 oz (Scandium frame, 357); the maximum round I want to shoot from that is a 158-gr. bullet running abou 900-910 fps--e.g., to the same criteria.
A 386 Night Guard (2.5" barrel, scandium frame, 7-shot, 24.5 oz.) can be controlled much easier with its L-frame.
As a carry gun, the advantage to the M&P340 include superior frame strength, noticably better factory fit and finish, and better (front) sight options. I carry that or my 360; either one has a boot grip on it. Personally, the 640 weighs too much for pocket carry IMO--but an underarm rig is fine for it.
Jim H.