I'm not sure about the culinary differences, but I've heard that mitten crabs are a bit sweeter (although I think they may have less meat).
As for why they're not more popular, at least in the US mitten crabs are considered an invasive species (i.e., they take over the habitats of the native species, like blue crabs, thus lowering the native population). While controlled harvesting of the crabs could potentially help slow the spread of the species, it also creates a conflict of interest among the fishermen. For example, if fishing of mitten crabs becomes more profitable than fishing of blue crabs, the market could naturally tend to preserve the mitten crab population. Therefore, it is currently illegal to even own a mitten crab in the US:
(2) The importation, transportation, or acquisition of any of the
species listed in this paragraph is prohibited except as provided under
the terms and conditions set forth in Sec. 16.22:
(ii) Live mitten crabs, genus Eriocheir, or their viable eggs;
Section 16.22 simply states that you need a special permit in order to keep mitten crabs, along with a special containment facility to ensure that none of them escape into the wild.