Sumiko MMT vs SME IIIs on Sota Sapphire

I've got an SME IIIs in a box. Is there any point in swapping out my Sumiko MMT tonearm on my early Sota Sapphire? Will I hear any difference? I'm used to using cartridges like Grados and Shures--nothing too exotic. I know I'll need a new arm board--just wondering if it's worth it.
Your choice of arm should be based on the cartridge(s) used, or vice-versa. Look for threads by Raul regarding the importance of matching cartridge and arm.

This begins with the arm mass/cartridge compliance optimization but based on Raul's experience, it can go further with specific synergisms.

At the time the SME III was being sold I recall that Shure was their importer so I expect that should be a good match. However the MMT might match well with a greater number of cartridges since it is closer to medium mass than the low mass III.
I keep going back to my original V15typeV and a new M97xE as they seem to be a good match with some of the older "not mint" vinyl I like to play. Those are medium mass cartridges aren't they?--are they better suited to the MMT rather than the SME IIIS? I'm a little confused if Shure was importing the SMEIII....