As consumers watch TV on a widening range of screens and devices, every player in the mobile and media value chain is battling to own the user experience, and therefore be in pole position to shape the business model. No contender has every weapon in place, so each has to play to its existing strengths. In Apple’s case, that means building on its apps ecosystem to mask its limited number of content deals; for Verizon, by contrast, it means harnessing its mobile network and integrating AOL’s advertising platform as rapidly as possible. Both these companies launched new TV offerings in the past week and they epitomize the battle between device platforms and network providers, to own a TV experience increasingly…