First attempt by Starship failed: https://en.wikipedia.org/wiki/SpaceX_Starship_orbital_test_flight

Blue Origin reached altitude of 351,232 feet but did not orbit the plant https://www.cbsnews.com/news/blue-origin-launches-six-passengers-on-supersonic-flight-to-the-edge-of-space/ If neither completes a full orbit by the end of the Question, it will be resolved on the basis of which reached the highest altitude.

Blue Origin launches six passengers on supersonic flight to the edge of space

It was the sixth crewed flight of Blue Origin’s New Shepard sub-orbital spacecraft.