Streaming of video contents over the Internet is experiencing an unprecedented growth. While video permeates every application, it also puts tremendous pressure in the network – to support users having heterogeneous accesses and expecting high quality of experience, in a furthermore cost-effective manner. In this context, Future Internet (FI) paradigms, such as Information Centric Networking (ICN), are particularly well suited to not only enhance video delivery at the client (as in the DASH approach), but to also naturally and seamlessly extend video support deeper in the network functions. In this paper, we contrast ICN and TCP/IP with an experimental approach, where we employ several state-of-the-art DASH controllers (PANDA, AdapTech, and BOLA) on an ICN vs TCP/IP network stack. Our campaign, based on tools which we developed and made available as open-source software, includes multiple clients (homogeneous vs heterogeneous mixture, synchronous vs asynchronous arrivals), videos (up to 4K resolution), channels (e.g., DASH profiles, emulated WiFi and LTE, real 3G/4G traces), and levels of integration with an ICN network (i.e., vanilla NDN, wireless loss detection and recovery at the access point, load balancing). Our results clearly illustrate, as well as quantitatively assess, benefits of ICN-based streaming, warning about potential pitfalls that are however easy to avoid.