In the end HTML5 will work fine on phones. That'll take a few years yet though; currently it's shit. It's ok on an iPad, but compared to native, not so much. I like
nice responsive HTML5 or HTML5 apps for stuff I use sometimes; like booking tickets, hotels, checking what's on TV and such. For stuff I click in all day long, like bugtrackers, PM systems, CRM, etc, HTML5 on mobile or desktop, is just wasting time. It's just not very nice to work with productively. This is improving fast on the desktop by building in provisions for being (temporarily) offline, easy drag & drop, offering small native plugins to interact with it, but it's not there yet.
On phones it's far from being a nice and productive experience; you can see that well when you 'quickly' check a task and end up trying to swipe something 10 times because it lags and swearing profusely. Which happens with all badly 'cross platform' written apps which are mostly HTML5.