Desktop apps got their lunch eaten by the web based purely on the deployment and portability benefits, the UX still lags behind to this day. Granted the app store model mitigates the installation pain, but portability is non-existent, so my hunch is that HTML5 will pick up steam over the long-term as mobile browser support and developer knowledge coalesces.
Interestingly I think a lot of apps could go HTML5 today, were it not for subtle issue of web pages being awkward on mobile. Bookmarks and google searches just don't have the immediacy they do on a computer, so the very fact that native apps are easier to get to is a significant hurdle in terms of user behavior, even if it is possible to develop a excellent mobile-browser-based UI.
It's possible Apple, Google, et al could parlay this into a longer dominance of native apps, but that raises two questions: do they really care enough to attempt to sabotage HTML5? and will developers put up with the hassle of the fragmented mobile landscape? It's unlikely any of them would cripple their mobile browser ala IE6 because web is important one way or another, but if everything shakes out to an iOS/Android duopoly then developers may decide the pain is worth it. So no bold predictions from me, but it's definitely an interesting question.