I don't post most birthday party photos to facebook because there are other people's children in them, and I don't really feel like it's my place to share those photos.
I do feel like it's oddly revealing and a little depressing when people post photos of parties and tag people in them so you can see that your friends were invited, and you know you are not invited because clearly aren't on that level of friendship with the person, but you didn't realize that until you see the photos.
I'm somewhat sensitive, however, and I've stopped having parties for my younger child. I've had three for my younger daughter and they weren't very well attended, although we had fun with the people who came. Sometimes my daughter is invited to the parties of those whom we invited, and they are packed. And then often they have parties and don't invite her, and I just don't want to have hurt feelings about all of this, so I figure instead of paying all this money for other people, I'll get her the gift she wants. If I throw her a party, that ends up being the gift.