SpaceX vs Blue Origin
SpaceX
1st to space
1st to orbit
1st to reuse booster that did more than a bunny hop
1st to stick a landing from a "real flight"
1st to stick multiple landings (today)
1st to launch, orbit, and recover pressurized cabin
1st to deliver meaningful cargo
1st to orbit a car (Only NASA has done that one!)
1st to produce 5 million lbs of thrust
1st to have 27 +1 nominal engines kicking booty
Blue Origin
1st to stick a landing (by about a month, from a dinky bunny hop)
1st to reuse booster (from a bunny hop)
There is no space race between the two at this point. B.O. has a lot of catching up to do. Blue Origin fanboys will claim they aren't behind because they just have different goals, but SpaceX already has the heavy lift capability to launch hardware for either company's goals.