Exactly - they are using FNPT II sims, built in a "737-style" flightdeck, with much of the "real 737" there, but solely for MCC (and JOC?) purposes. It is not a Level C/D 737 sim for TR purposes by any means imaginable, and is not certified to a level to my knowledge per CAA records.
FTE have a real sim - Hawker 800, certified to Spanish CAA L2B.
You have to think though - what is the purpose of the sim, is the Oxford one going to give you a real "glass cockpit" exposure being only FNPT II etc, and indeed, do you really need that for what you are using it for?
One is bulit for purpose (Ox), while the other might be more similar to one used for sim check (FTE). Are you going to get any useful experience though in the real one at FTE - possibly not.
A CRJ sim (presumably as few people are flying CRJs at the moment, so they are cheap and available) would probably be more real.
Frankly, you could do MCC in something cheap and nasty if you wanted - they are just tempting you with bells and whistles!