Sauerkraut for hot dogs
It really comes down to taste. In this usage, you're treating sauerkraut like a condiment so there's not really a "correct" answer.. A lot of hot dog places have traditions - for instance, Nathan's Famous hot dogs (the original "Coney Island" hot dog) uses these combinations with kraut:

-Sauerkraut, spicey brown mustard (New York style)
-Thousand island dressing, sauerkraut, swiss cheese (Reuben style)

A famous hot dog maker in Pennsylvania, Yocco's Famous Dogs, uses sauerkraut and a thin bean chili combination to make their hot dogs.

The sauerkraut will often be very strong tasting, but not as "funky" as kimchi. It pairs well with a lot of different foods, usually other strong flavors (either strong tart like the spicey mustard, or strong sweet like the thousand island dressing or sweet relish).

Personally, I just eat sauerkraut with a fork. But if I have it on a dog, I pile it on with dill relish, country style dijon mustard, a dash of sriracha, and some diced onion. I recommend not kissing anyone for awhile after eating.