I’m starting to think this advice may vary depending on the strength of your undergraduate training. I.E. did you do art history at a well-regarded school (and did you write a thesis?) or did you major in something else or otherwise not feel completely prepared for a PhD? I have always been told the path to a good PhD is Williams or the Courtauld. Of course, if you feel like your art historical foundations aren’t entirely solid then a two-year American program is most likely going to teach you more than a one-year British program. If, however, you feel pretty comfortable with where you are academically then it seems to me hard to beat the seal of approval the Courtauld provides. I’ll be going to the Courtauld. That said, I can also understand arguments against it, particularly if it comes down to funded-at-Tufts vs not-funded-at-Courtauld.
(FWIW I have heard people say a Courtauld/British PhD is less respected than an American PhD, at least in American academia, so I don’t know if that’s confusing matters?)