A small step forward:
In the upcoming version of SharePoint 2016, Microsoft has made some advances in the mobile department. Yet, I feel they have still missed the mark. For anyone on SharePoint 2013, you will see some changes in the mobile touch view... allowing you to control and manage documents a bit better on your mobile device. However, it's not quite the mobile experience I think SharePoint 2016 should have, especially given the very mobile-centric world we live in.
Not to say you shouldn't upgrade-- you definitely should. SharePoint 2016 has introduced a ton of new features, including large file handing, zero downtime patching, unified search and much more!