Both Sauerkraut and Kimchi are cabbage that has been cooked and fermented so they're essentially the same thing.
However there is a difference between the two and the main differences are the way it's cut and the ingredients added to the cabbage.
Kimchi is cut into larger chunks and includes plant leaves and stems as well as hot Korean chili pepper, garlic, and fish sauce are added for flavor.
Sauerkraut is also fermented and cooked cabbage but without those additional ingredients added to the cabbage.
They're both very delicious but I do prefer the Kimchi for a better taste than Sauerkraut.