He sat at the feet of his professor.
He sat at his professor's feet.
If it's a literal statement, I would say both are equally common, and equally valid. In some "metaphoric" usages, such as...
...the first version is far more common. Probably because the more verbose form adds a touch of "gravitas" (makes it sound more formal). But in more "homely" contexts, such as...
...those second forms are virtually unknown. So I would say only use the possessive apostrophe in these constructions when it's an informal/personal context.