Are both fundamentally not the same thing? I understand that company A may have made you a bit uncomfortable, but perhaps their intent was the same as company B's? That is, to see how you logic out a problem. You did say that you got the job in the end, so clearly the point wasn't to see if you knew some APIs by memory as a make-or-break situation.

There's also some benefits that can be gained by company A's method ostensibly over company B's. You get to see their response to the discomfort of not remembering an API. You get to understand their problem solving abilities, not in terms of code, but in terms of interpersonal relationships. In a recent article I read, someone had suggested offering a code prompt and then challenging the applicant to find the bug on completion (even if there wasn't one), simply to see how they respond when faced with that challenge.

Naturally it may not be perfect, it's just hard to really quantify which one is "better" if they're arriving at the same end -- a presumably competent engineer being hired. Are companies not interested in hiring people with both interpersonal skills and technical ability, after all?