We don't know, but given we can glimpse into the playtests of both BF and 1D&D, I'm going to say they have more in common than KP is willing to admit. BF was made to sound like it was going to be 5e with replacements for the stuff not in the SRD, but KP began to tinker and Surprise! they are making the same types of changes WotC is making.
Racial ASI: gone.
Feat/Talent at 1st level.
Race having cultural elements moved/siloed.
Unified spell lists
Greater access to inspiration/luck
New class features
Subclasses having a unified progression (possibly, we have limited reference in BF, but the wizards subclass features were moved to match the fighters in the limited info we have)
Spells, talents/feats and other elements are revised.
As far as using supplements like Xanathar or such, you're going to need to do the same amount of conversion to make it work with BF as you will with 1DD. I'm sure you will be able to run a 2014 fighter, a BF wizard and a 1D druid at the same table in the abstract, but each one is going to end up needing some work to be compatible. In that, BF is Two D&D, One D&D's brother from another mother.