"What are the major differences when EU pilots do sim training compared to UK pilots?"
Admin only. It's possible that with time the UK CAA might diverge from EASA but right now the content is the same. if you want some light hearted entertainment, download the EASA Differences Document (published quarterly) then choose six different NAAs at random and see how the admin requirements vary for LST or LPC. When working as a TRE in an EASA airline with 20+ nationalities the admin was the most challenging part (along with the fact that frequently I was the only native English speaker in the room and the two candidates could be of different nationalities being examined in their second language with no first language in common!).