No one that I am aware of is specifically 'in the know' on this, but speculation seems to be it'll be by boarding group. Since BE fares are all in the last boarding group (presumably, it will be something like group 6), it should be pretty easy to police - once they call this last group, no one can bring the bigger size carry-on.

In another sign the speculation is correct, elites on BE fares are specifically exempt from the carry-on restriction, and given they do get their elite boarding benefits, makes even more sense that this would be the case.

Of course, whether they went too far on this or not is a different story. I get it, but in general, on most flights that are full/close to it, those in the last boarding groups are probably not going to get overhead space anyway. DL does not restrict folks from bringing on carry ons by the rules on E fares officially, but in practice in most cases, DL non-elites, like those on UA in BE, board last, and therefore will generally have to check their bigger carry-on anyway as their is often no room in the bins by then.