Skylon's rockets can switch from air breathing to internal O2 tanks. It liquefies the incoming air in under a hundredth of a second and pumps that to the rockets. Or at least it will when it's built.
"When"? No: IF. And I can't stress how BIG that "IF" is. Compared to SpaceX and the Dragon V2, Reaction Engine's Skylon is all but vaporware. The Skylon is to space-access what the Moller Skycar is to flying cars. Actually it's worse; at least the Moller Skycar actually has had (slightly) successful tethered flight tests. They have successfully tested the engines for the Skylon, but Singe-Stage-To-Orbit is so much more than an engine test.
SpaceX has successfully demonstrated landing a liquid rocket on the Grasshopper....Reaction Engines has a static ground test of their bare engine.
No, the Dragon V2 if anything is "double hearted" when compared to the Skylon.