Similar issues with a 15 mnth age gap. Dd has just started in reception but has a late Aug birthday.
Ds sometimes teases dd about what she cannot do - the bossy and bragging thing that you mention - we explained that when he was exactly the same age as her, he had not even started school so in some respects she is way ahead of him.
Sometimes they play games on the Cbeebies website. However, a condition of allowing ds access is that he shares with dd and helps her. Would not say this works perfectly though as ds bosses dd around (a lot).
We also took the tack of making clear that dd understood that there were advantages to being younger too - there were things that she could do that he could not (play in a particular soft play area, be picked up be me etc).