The version on Steam is essentially the mobile version, but tuned for desktop and laptop screen sizes (I ran it on a 30 inch iMac, but it should run on a 1024 x 576 netbook). HeroCraft has been responsible for the Steam versions, since I’ve been busy with Six Ages, so I am not completely sure of the specifics. But I believe the Steam achievements are the same as those we added in 2.0. There are also Steam Cards (which may have some new art).
So if you played on Windows or Mac before, you’d be moving from 1.7 to 2.2. There are 48 new scenes and 4 new illustrations (plus a new Lore map). There are also new advisors, and a lot more advice in management screens. There are also more treasures. We made many bug fixes (such as unblocking two of the original scenes), and fixed typos. You no longer have to worry about sheep. The economics system should no longer be quite as harsh, with death spirals less likely. (Rest assured that the game is still difficult, especially on the Hard setting.)
The Tula screen was too difficult to rework, but it wasn’t part of game play. And HeroCraft originally started their porting before our scene contest, so those scenes are currently only in the iOS version.

So if you have played King of Dragon Pass on a laptop or desktop, but not a mobile device, there’s a lot of new stuff. And if you haven ’t played at all, now’s your chance!