Adam Mintz has written a fine essay called The Talmud in Translation, in which he elaborates on the history of the Artscroll, Steinsaltz, and Soncino Talmuds and the various polemics concerning each.
Regarding "rejections," there have been critiques for each Talmud.
On the Soncino, there was a little controversy that concerned making the Talmud accessible to non-Jew if it was translated.
On the Steinsaltz, many in the charedi world followed R. Schach's condemnation because "it was
written by the same author who penned several books that they considered to contain words of heresy." Regarding the translation, R. Schach disapproved of its modern Hebrew translation and the "secular" style of its study aids.
These issues are just as relevant for the Artscroll Talmud, but perhaps their haskamot from R. Elyashiv and R. Schechter have opened more doors for chareidi acceptance.
Like Charles Koppelman, I disagree with your premise that the Steinsaltz and Soncino Talmuds "have not received anywhere near the same levels of support." See, for example, the powerful haskamot reprinted in the new Steinsaltz translation. I know many in Israel prefer the Steinsaltz over the Artscroll, and there are various reasons, such R. Steinsaltz pedagogic honesty on translating controversial statements in the gemara, the encyclopedic information to facilitate study, and a general method of providing the tools to start digging rather than do all the work for you.
This is popularity is certainly true in modern orthodox/daati leumi communities. I mention this because I personally believe political divisions between the daati leumi (which many identify R. Steinsaltz under) and chareidi (e.g., Artscroll) world have a lot to do with this discussion of acceptance.
The Soncino, however, might lack the same contemporary support simply due to antiquated aesthetics, lack of study guides, and more archaic translations in comparison to the other two.