In case you want to play a terrific space game before the release of No Man's Sky, there is one that you can play now called The Solus Project. It is a game available on Steam now, and it is also available for the Xbox One. The release date of the game makes it seem like it is made to compete with No Man's Sky, and it is possible that it is more than just a coincidence. So, yes, The Solus Project could be a smaller scale No Man's Sky for the Xbox One.
The Solus Project is about how Earth has essentially gone the way of dinosaur, and so humanity is left up in the air (or up in space), and the human race has colonized near Pluto. The game may not have the possibility of exploring 18 quintillion worlds, but you can explore one definite planet. The planet that the player finds him or herself on is more distant than Pluto, which is called Gliese-6143-C.
Engadget reports how Xbox Wire states that the player needs to unravel the mysteries about what happened to the human race. You can survive the hostile environment of this planet, as well as find a way to signal home and essentially save humanity. According to the game's official website, you can survive through exploration, including the depths of the uncharted planet, with "huge cave systems and tombs and uncover over 200 secrets".
The Steam Store (which has the game available for $19.99) states that The Solus Project is a spiritual successor to The Ball, which was the 2010 PC Gamer Action/Adventure Game of the Year. The game's website says that it takes place in the "same universe, same backstory, same atmosphere".
So yes, the game is not No Man's Sky, but from what it sounds like, very few games are like that. Not only that, No Man's Sky is only available on the PS4 and PC, so if you want some space exploration on the Xbox One, this is the way to go. The planet has such a rich atmosphere with temperature, humidity, wind, ocean tides, storms, earthquakes, and plants that respond to the environment.
As mentioned before, The Solus Project is available on The Steam Store, and it will be available for $15 on the Xbox Store at the end of June. By the way, this game is going to have support for Virtual Reality for both the Oculus and the Vive. Granted, this is a work in progress for the game, so there isn't quite a formal release date for that.