Responsive, HTML5, javascript pages are great and work on any PC, tablet or phone and yes HTML5 can do some amazing things. We once wrote a system in HTML5 that tracked my movements in real time and I could see where I had been on a map. It is certainly a powerful platform. The short answer is it depends on what you want to do and where you want to access it from. Mobile data connections are also unreliable outside city centers, and this generally moves you to a local storage solution where you hold the data on the device.

Another important issue is how much data storage do you need for your application. This varies by browser (and versions) and is generally reliably less than 5mb. ( Some browsers will randomly delete data when they need more space ) If your requirements for images and data are less than 5Mb then a HTML5 web page may be the solution for you. Just bear in mind that your site has to work on many browsers and there are sometime surprises on new releases. For example, the recent chrome 54 release in November changed line heights and text sizes on one of our existing web pages. Microsoft holds significant market share with their IE and there are many forums on the web discussing IE and its quirks.

For business applications, Apple apps are reliable and enable you to store much more data on your device ( limited by the size of your iPad memory )

Again it depends on your requirement as to the best path to take.