...what would it bring, and how "different" would it be compared to all others?
For myself, mine would combine the simplicity of ZetaBoards and the power and stability of Xenforo. It would be open-source too. Also that I would introduce Markdown as it's becoming more of a thing now and, I actually prefer it over BBCode these days. The name for it? Sophisto 😀 (name being a truncation of "sophisticated", btw)
In the initial stages of building our new community, one of our programmers was thinking about building a forum software because he hated all the "out of the package" stuff out there. That's a big project though, so we just went with Xenforo because of it's similarities to vB4, our previous software.
If I was doing something like that though, I'd be going for something that looks way nicer, sleek modern design. One of the things that annoys me about Xenforo is that it doesn't come with the ability to allow mods to ban people. I had to inially introduce an infraction that gives enough ban points to autoban for 14 days, before finding another solution.
Supermoderators on vBulletin had access to their own mod CP, which was a much more restricted version of the admin CP. They could temp and permanently ban, view both ban lists, run IP scans, create forum announcements among other things.
I would build one that's a hundred times faster than the competition, so it doesn't choke on a few bots, while keeping things simple looking, and I would have integrated analytics. Just like I've done in Gosora, actually.
And Markdown isn't all it's cracked up to be, I support it, but every site seems to have it's own flavour of Markdown, Jeff Atwood tried to somewhat standardise it, but the creator of it gave him the middle finger and thus, things are still fairly fractured.
With BBCode, everyone just copies vB, that is the definitive spec at this point.
On a side note, if you throw feature ideas at me, you might very well find those features getting implemented, very quickly too.
