Potential consequences of the UK Research Excellence Framework (REF) for US job prospects
The REF credits departments for grant capture and not the individual. This means that large grants with multiple PIs tend to be prioritized over smaller grants to individuals. In terms of the US job market, being able to demonstrate grant capture at the individual level is important in many fields. For example, generally in the US being the only PI on a $200,000 grant is viewed better than being one of ten PIs on a $5,000,000 grant. 

The REF "requires" academics to "produce" 4 high "quality" publications over a 4 year period. Only the 4 "best" publications matter. This results in a push for splashy, as opposed to solid, research. The goal for the REF is to make your work look important to people peripherally related to your field and not the people who specialize in your subarea. Authorship across the 4 publications can also be shared so teaming up with a more senior colleague and being a secondary author is very desirable for the REF. For the REF, someone who is a co-author on 4 Nature papers with colleagues at different universities, and nothing else, could easily get a position as an associate professor, if not a full professor. In the US, search committees want to see a body of solid work that is clearly done by the applicant.

Being able to demonstrate impact is also important for the REF. This requires wider engagement with people outside your field. Having research that can be link to a "change in process" is key for the REF. For example, a clinical trial that shows X is better than Y would be considered "high impact" while the development of X would have less impact. Blue skies basic research has essentially no impact and is discuraged. US job searches do not really care about impact.