The main difference I can point out is that the Model 10 is on the K frame and the 30 & 31s are on the J frame (early ones on the I frame), which is smaller than the K frame.
The K frame is the frame size that 38 Specials and 357 Magnums are built on (6 shot) while the J frame is normally for the 5 shot 38s, 32s, 22s, etc.
Also, and I'm no expert on these so I am subject to correction, I've never seen a K frame in 32 S&W, only in 32 WCF (32/20). NOT saying that they don't exist, I've just never ran across one.
As far as my pick of the above guns in 32, I would like to find either a 30 (round butt) or a 31 (square butt) for a fun little plinker. I'm becoming more interested in 32 caliber guns, having used 38/357s all of my life for general plinking duties.
I'm sure others with greater knowledge will be along shortly to chime in, but those are my thoughts.
TRE