Coming from a board gaming background, I'm curious how much of a leap is it from Dust Tactics to Dust Warfare?

I would say it's somewhat significant. I've never played Tactics, but I have the starters (and hence the Tactics rules) for the figures. From what I've read and seen, it's a fairly different game. The absolute basic mechanics are more or less the same, but there are a lot of differences. Additionally, you need a larger play surface, and terrain.

There are a few new concepts to grasp, like free form measured movement and terrain abstraction. Dust Tactics is actually a simplified miniatures game disguised as a board game, so in reality you are half way there already.