Mobile Websites vs Apps?

Mobile Websites vs Apps?
Earlier this week a school claimed that there is no need for an app given that websites are ever more responsive and able to provision for mobile devices.
Obviously when faced with such a response Appsforschools.org.uk are not bullish sales professionals who enjoy an argument, so I retreated politely.
However the statement made me question the value of mobile websites against an app.
My first thought was to question my own sanity.
If this particular school was so insightful about apps compared to mobile websites...how stupid must appforschools.org.uk be.... and for that matter how short sighted are the following websites:

all of whose apps I have on my phone rather than accessing their mobile website....?
But then I did some actual proper research rather than become embroiled in childish sarcasm....
According to http://techcrunch.com/2015/06/22/consumers-spend-85-of-time-on-smartphones-in-apps-but-only-5-apps-see-heavy-use/#.6mbxd0f:5bJy
Today’s consumers are spending over 85 percent of their time on their smartphones using native applications.
Secondly as yet, websites are still fundamentally passive media...sitting waiting for visitors to arrive.
Apps offer the facility for free and unlimited push notifications to communicate directly and actively with your community.
Finally, in an app the content is provisioned directly for the mobile experience, not simply sized accordingly....the content you see is the content you are most likely wishing to see on your mobile. In addition you can upload notes and progress - the experience is so much better in an app than on a website.
So there you have it a quick response but I wanted this to stimulate the debate, please tell me and all those big websites I mentioned earlier that we are wrong about Apps triumphing over mobile websites.
I really do want to hear the counter arguments.

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