Anti-seize is intended for use on surfaces that typically do not move against each other when in use. So using it on BB threads will be okay. In general, anti-seize is just grease with other stuff in it. Powdered nickel, aluminum or copper typically and some other stuff.

Grease however, can serve both roles. It is good for use on surfaces that move against each other or for surfaces that don't move against each other when in use.

Except for some few dissimilar metals in certain environments, bicycles don't typically experience the extremely high temperatures. Nor are their components made from materials that are prone to galling when being threaded together as are some other things.

So grease is fine.