And, there are (currently) two 360s
one is 38+P only, the other is 38/357.
Discussions of the two's differences can be found
here, in the M&P 340 thread.
The primary difference, then, between the 360s and the 340s is the type of action--SA/DA, with a hammer exposed, and DAO, with no exposed hammer. Personally, I prefer DAO for carry.
I assume you will want to carry your 'snub nose'--and if you have already committed to the idea of pocket carry, then that capability is the forte of these particular j-frames. If you are NOT committed to pocket carry, then there are innumerable other short-barrel revolvers to consider. For example, check out various S&W
Night Guard revolvers--these have the Scandium frames, short(er) barrels, but in other frame sizes.
added on edit: The 340PD, with its titanium cylinder, has had some problems, I understand. Apparently, the coating on the chamber walls of the cylinder can be scratched, leading to (at least) hard extraction. S&W has serviced these with no problems, but for at least one owner, recommended installing the M&P 340 (steel) cylinder.
The real plus of the 340PD--with its 2oz lighter weight, might show up for people needing a BUG in ankle carry. I know of
no one who routinely shoots 357 factory rounds from the PD, and there are few who shoot them in the M&P340 / 360 Chief's Special. A j-frame in this weight range is really a 38+P handgun, IMO.
Jim H.