Are the criteria of faculty positions different in the US and UK?
There are several levels to answer your question. 

There is a large variation in quality in both US and UK institution, from world best to the end of the spectrum. We do not know - and you can only rely on available university ranking - if both US and UK institutions you applied to  lie in the same range.

Now, statistics. You said you applied to 5 jobs in US and got invited to 3 interviews. Applied to 4 UK jobs and got 0 interviews. If we use the hypothesis that US and UK institution quality is the same, then your average success rate is 3/9=33%, and the chance to get 0 interviews instead of the (less than) 2 you would expect could be entirely due to randomness. I see no reason to think of biases to start with.

You do mention that one UK position has been reopened, which means that they thought you did not meet their requirements. Which leads to the requirements issue: I would find it unlikely that all 9 institutions are looking for somebody with the same profile. Perhaps some institution care more about teaching, others about the ability to get grants, other about seniority in the field, etc.etc.

Last, you say "I prefer to move to the UK since I still do not need a work permit". US institutions are eager to sponsonr visas for people they wish to hire - and the government makes it easy to issue visa to academics at any level; you certainly need not worry for a full professor position. And with academic visa you can get a green card in a short as a year. They'll probably pay for relocation as well.

Moral: I am not aware nor is reasonable without data to say that there are fundamental differences in general criteria for hiring faculty between US and USA. There are certainly large variations at both university and department-level strategies. Visa is not a problem at all.