Is there a different Profile Manager for the second profile? Then it's a question of who gets there last, gets to do the merging, and will be presented with the side-by-side. When you are just comparing them (before the merge actually takes place) you are just viewing them, not merging them, You aren't missing anything, because there isn't anything there to miss.
When you are picking which bits to go into the final profile, you don't pick one side or the other. You pick every single fact, like: name, date of birth, place of birth etc. like
Date of birth: 29 November 1603 or 28 December 1603 - so you pick which one is right.
Place of birth: Yeovil, Somerset, England or Exeter, Devon, England. You pick which one is right.
And so you go, right the way through the profile. You don't just pick Profile A or Profile B in its entirety.