You may have noticed that certain wedding invitations request the pleasure of your company, others the honour of it, and still others, the honor.
Here’s what has been the rule of thumb for nearly forever. If inviting a guest to only a reception, request “the pleasure of your company” because a reception is considered a social event for pleasure. Typically, we use “the honour of your presence” if inviting your guest to a religious wedding ceremony. This is because a wedding ceremony is A BIG DEAL, so it’s an honor rather than a pleasure to have them there.
Historically, Americans opt for the British “honour” over “honor” on wedding invitations. It’s even expressly stated in Emily Post’s first etiquette book to use “honour.” It’s likely because us Americans often view the British version of English as more formal, but I can’t imagine this usage will stick around much longer. The same goes for the “favour of your reply.”
However, if you’re hosting an extremely formal event, these days “honour” will likely help you convey that. Otherwise, choose whichever you prefer. Both “honor” and “honour” are correct.
There you have it.
It's good etiquette to share what you like!