I think this is one of those examples of a fan base taking an off-the-cuff comment much too seriously. Here's the original, brief context from the DimeBash interview:-
Eric Blair - "Does this harken back to the Mechanical Animals era, or an era before that?"
Twiggy - "Uh, it's kind of like a, it's a little more of a punk rock Mechanical Animals."
I don't think Twiggy would have referenced Mechanical Animals specifically, had Blair not already injected it into discussion of Born Villain.
There have been a few stylistic comparisons between the two records, alongside Manson stating during interviews that Born Villain was recorded in a sheer white recording space, as was Mechanical Animals, but I don't think there was any intentional or conscious effort to reflect the former album in the latter. Similarly, had Twiggy been asked about any record he was part of in relation to Born Villain, the likelihood is he'd have spoken favourably of both, because that's what artists do when speaking with candour. Fans, however, get hooked on words far too easily, and stretched that one brief comment to mean something entirely other.
In basic terms, when put on the spot comparing a new album with something from the past, the easiest solution was just to say there's a more serrated, caustic vibe to the music, which there is. Overall though, besides Marilyn Manson being a band with a signature sound (quite the mean feat considering how many personnel changes have occurred), no one album sounds like another.