Yea, Weddings aren't something you invite everyone you ever worked with just because you've worked with them. As far as Tennant, there's lots of news indicating they have a close friendship, so, it's natural he'd be invited.
Heck I know people who don't invite people they work with now to their weddings! I can see Eccleston in a work environment taking things too seriously, and I can also see Barrowman not taking things seriously enough so that kinda makes sense. I suspect they're oil and water.
I remember in an interview done around the time of the S3 finale arc, Barrowman was asked to compare working with Tennant and with Eccleston, and he said Tennant was a "happier person" than Eccleston. But that's all I remember hearing about the working relationship between the two.
I don't know that Eccleston has ever spoken about working with Piper. Piper, on the other hand, has occasionally said things about working with Eccleston. Nothing bad. In comparison to Tennant, she found him to be very professional and very serious.
Maybe he was invited but he decided not to come for personal reasons he chose not to disclose to anyone.
Being serious, that's entirely possible, given his dislike of celebrity-ism, and the likelihood of papparazzi trying to gatecrash in on Billie's wedding. Can't remember if they did, but he might just send a polite 'Sorry' to avoid the chance. Oh, and if Moffat was going to insult him, it'd be a "Soft Southern bastard." Moffat is from Glassgee, after all, and to them Salford's so far south and softy it might as well be in London :
At this point I'm beginning to wonder why any of this is owt to do with us? I mean wedding invites, working relationships, aren't these basically nothing to do with us?
Obviously it has everything to do with us. There is no other reason Al Gore could've invented the Internet(tm) for, aside from so we SciFi geeks could speculate and gossip about every little thing related to our shows, sheesh
Just imagine what they'll say when none of you lot get an invite to our (RevdKathy & I) wedding. I must absolutely loath every single one of you.