@Robert-Jan as usual a very nice article about the movie and Omegas participation in the project.
Having seen the movie three times, and embarrassingly the third being almost exclusively for watch spotting, I think the movie gets real close to accurately showing period correct watches as worn by the astronauts during that time period especially the use of the JB Champion bracelet which would be a first in a movie and nice to see.
Ed White's wrist clearly receives the Oscar win for the JB Champions performance on the wrist of a major character. Unfortunately I think Armstrong looses and Aldrin isn't even nominated. While Armstrong does wear some type of period correct band I'm not completely sure it is the correct JB mesh bracelet. Something looks off in the mesh pattern and the end links in the movie. I can't say definitely and I think only a Blue-Ray viewing with solve the mystery.
Aldrin clearly does not wear the correct bracelet and it's even more evident in the movie when he is seen from the rear in the pre-flight press conference.
Here is a picture from Universal/Universe Today showing the press conference where Aldrin's incorrect bracelet can be seen. Collins gets the short end on the stick in the movie but he does seem to get a JB style bracelet judging by the release clasp on the bracelet.
All in all, I think the the prop and costume team did a great job portraying the watches of the period. With a budget of 59 million dollars sourcing a few additional correct bracelets wouldn't have broken the bank.
It does have to be somewhat disappointing to Omega that the best scene of the Speedmaster being strapped onto the wrist of Armstrong, as seen in the Omega video, ended up on the cutting room floor.