It's not either one or the other. Anki is a supplement to input received from native speakers and media. The idea of spaced repetition is to help one efficiently remember the thousands and thousands of words needed for a sophisticated vocabulary.
I definitely don't recommend anyone to try and learn a language from e.g. Anki only.
Indeed it's not one or the other, but if Krashen's "comprehensible input" theory [1] is (mostly) true, the role Anki (or any SRS system) or grammar books plays would be very small (if not non-existent), and many polyglots' opinion on Anki seems to back it up.
I definitely don't recommend anyone to try and learn a language from e.g. Anki only.