I Am Not A Lawyer, but what immediately jumped out at me is how the patent grants seem very different between BOML and permissive-next.

BOML states merely:

Each contributor licenses you to do everything with this software that would otherwise infringe any patent claims they can license or become able to license.

permissive-next by contrast states:

1. Subject to the terms and conditions of this License, I grant You:
...
b. A non-exclusive, worldwide, perpetual, royalty-free, irrevocable patent license under Licensed Patents to make, have made, use, sell, offer for sale, and import Covered Works.

"Licensed Patents" means all patent claims licensable royalty-free by Me, now or in the future, that are necessarily infringed by making, using, or selling My Work, and excludes claims that would be infringed only as a consequence of further modification of My Work.

"Covered Work" means My Work or a derivative work of My Work. 

Your license grants under section 1 are automatically terminated if You initiate a patent infringement litigation claim (excluding declaratory judgment actions, counterclaims, and cross-claims) alleging that any part of My Work directly or indirectly infringes any patent.
 
Termination of Your license grants extends to all copies of Covered Works You subsequently obtain. Termination does not terminate the rights of those who have received copies or rights from You subject to this License.
 
To the extent permission to make copies of a Covered Work is necessary merely for running it, such permission is not terminable. 

As far as I understand it, then, BOML's patent grant gives licensees (be they users or creators of derivative works) patent licenses, in fact even more broadly than permissive-next if I'm reading that right? I'm not entirely sure how broad the scope of the BOML grant is; "can license or become able to license" [emphasis mine] sounds like it could have theoretically unlimited scope!

By contrast permissive-next:
  • Grants fewer but IMHO far clearer granting of patent rights; notably it draws a boundary at any additions to the work, only covering the work as provided by "the individual or legal entity that places" the work under permissive-next. 
    • In other words, at least as I understand it if Entity A owns patents 1 and 2, and the work as provided to the public under permissive-next includes stuff that would fall under patent 1, Entity B could take that work and be confident they would not be infringing patent 1, but if Entity B adds functionality that would infringe patent 2 the patent grant would not then apply to patent 2. 
    • It seems to me that in this scenario if the work was under BOML this might be quite different, and patent 2 would in fact be covered under the patent grant, which while arguably positive from a "software patents, they're bad!" perspective, is oddly viral (so to speak) for a permissive license, and seems like a pretty big blank cheque to write.
  • Terminates your patent license grants if you initiate patent infringement litigation against the entity you got those grants from via the software license.
    • So, if Entity B owned patent 3 and figured Entity A was infringing on it with The Work, if they then sued Entity A over this (perhaps as retaliation for having been sued over infringing patent 2) they would lose their license for patent 1 for their Derived Work. No such termination would take place under BOML.
I could be really misreading this all; as aforementioned, IANAL! But it sure seems to me that permissive-next and BOML are very different licenses in terms of just the patent grant portion alone. And as the patent grant portion is a core part of copyleft-next, it would make no sense for copyleft-next to sunset into BOML. 

And in addition, as aforementioned, I find the wording in BOML very unclear and ambiguously broad, which is a serious problem when you're trying to convince people to use a new license. To editorialize a bit more, one of the big upsides and selling points of copyleft-next is that it tries to be legally comprehensive while still being easily readable by baseline humanity; BOML by contrast seems to err far more on the side of brevity, arguably to the detriment of clarity.