I feel cross-platform stuff is currently a mess- no matter which path.I just spent a lot of time working on tools for all of the above plus we needed a SaaS/web version. We used AIR and Flash but be prepared to hear the "Flash is dead" phrase from the peanut gallery, including investors. You didn't mention the need for a web-based version so that makes Qt a possibility for you.
I agree with John that cross-platform UIs can cause problems but I don't think this is always the case. Some applications do lend themself to more standard native UIs but others do well with a custom look across platforms. Spotify uses embedded Chromium for cross-platform and web apps. This is an option too but a not a mature and proven path. Which means the safest assumption is there will be some engineering headaches in doing so.
Personally, I couldn't fathom actually trying to manage seperate code bases for: Windows, OSX, iOS, and Android. I can't help but think you'd spend more time coordinating than developing new features.
Last question- do you really need to be cross-platform? Sometimes it is better to nail it on one platform rather than spread resources. In my case, unfortunately, this was not an option.
In summary, I felt working across platforms (mobile and desktop) was a 'damned if you do, damned if you don't process.' Compared to the web development many of us are used to- writing one server version and tweaking for different browsers- it really seemed a pain to me.