I’m in Mexico for the next two weeks so do not have access to my melodicas to compare, but I don’t think there are significant differences between the M-37 and the M-37C, in the reeds or otherwise. A tapered reed is narrower at the open end than at the base.
The Suzuki Pro 37v2 has tapered reeds, while the M-37C does not, if I’m remembering correctly. But this doesn’t seem to provide any sound advantage.
3 June 2018: I noticed today while shopping at Amazon Japan that both the M-37C and the M-37C Plus have come down in price, and the Plus model is only about $10 more than the regular C. The M-37C Plus is available on eBay with “free” shipping from Japan for about $130.