IMHO the question is rather what audience do you intend to reach? If you are targetting mobile devices or Apple products, then HTML5 is definitely the way to go. AFAIK the time horizon for Flash support (even with the last version of Flash Mobile just being rolled out) is 1 year. Even for desktop applications, I don't know whether Adobe will make another 'flash' annoncement discontinuing support in the near future.
In addition, HTML5 is not that different from its predecessors. The 'main innovation' is the
Ok, rants aside, I have two projects and we are just at a turning point, meaning, we have clarified the specs, but no coding has been done, so we can (relatively) easily change the dev tools. In both projects, the technology to be used would've been Flash. But now, we will opt for HTML5. I am not going to hide the fact that we faced pressure from other participants in our project to switch.
It is true that HTML5's support is not a solved question and it will probably remain that way for some more time, but with Adobe dropping support, pressure to get things straight in that department is bigger.
I admit that certain things were much easier to do in Flash and that a shift to HTML5 might be problematic for advanced features and probably your management sees it as a waste to leave that expensive software unused plus to invest any effort for the shift... But that's the way things go: who cannot cope with the change, is doomed.
Now on the user experience/usability end of things I believe it will be a bit of a rough start with the patchy support ther is right now, but if the product still needs to be there 3 years from now, I think HTML5 is a safer bet.