The X-37B is a redesignated X-37. It was originally a NASA project, part of the Reusable Launch Vehicle program in the 1990's along with the X-33, X-34, and DC-X. None of these vehicles were intended to be operaitonal. They were designed as technology demonstrators, to test propulsion. structures, aerodynamics, guidance, navigation and control and thermal protection concepts for a new generation of manned space shuttles that would be fully reusable, practical, and safe. In other words, its original mission was to help develop a real "space taxi". Sean O'Keefe and Mike Griffin don't seem to have understood that human spaceflight is much to expensive, and stamped out all NASA work on modern reusable launch vehicles. It's good to see DOD recognize the value of reusable launch vehicles, but it's disappointing to see NASA become essentially irrelevant in the development of advanced launch vehicles.
The X-37B is also a technology demonstrator for a reusable launch system. It makes no sense to talk about its military mission; its mission is simply to develop the technology for an operational reusable spacecraft that will be a transport for launching and retrieving orbital payloads. AS a technology demonstrator, the X-37B was made as small as it reasonably could be and still provide a valid test of the technology. It is too small to carry most DOD payloads, so an operational vehicle will probably be larger. As to the V-tail, the Shuttle vertical fin is in the wake of the fuselage during much of the hypersonic entry and so not very useful. More important is the long control moment with the wings forward and tails aft, which gives it much greater pitch controlability and CG range than the delta-winged shuttle.