It runs more stable on Xbox One than it does on my GTX970 PC (Obviously doesn't look as good or achieve as high frames).. but judging on overall stablility it's better.

I've had crashes on Xbox but they are not that common... This game has by far the most community engaged developers of any early access game, it's insane the amount they add very regularly, and most of it based directly on player feedback.

It is really fun. Performance is slacking though, I can't tell you definite numbers but I can give you examples:
In open areas with lots of Dinosaurs like when at a tribe base with even a few people around the game suffers small lag spikes.
When at the swamp biome area of the island, the game suffers lag spikes here and there. I can't say consistently but they happen a bit more often than when at, say, the beach on the Southern Islets.
When walking into a cave by yourself, the game shoots up to a very smooth, steady, consistent FPS probably because the lack of other players and their connections bogging down the server loading creatures for everyone.
Auto saving that occurs will slow the game down for 2 or 3 seconds at most.

All these observations are from Official Dedicated PvP server. In single player things are a bit different:

Game runs more smoothly by a few frames. Probably because you aren't trying to maintain a connection with a server to 70 other players.
The connection you have almost never bogs down or gets a High Ping.
You have complete control over how the game behaves like XP gain and dinosaur respawn and such.

The game needs work bringing visuals up to par and more complicated visuals giving a more engaging experience as well as dealing with lag spikes resulting in high Pings and even disconnections