Adolph Weinman Design

Sure there are obvious similarities but also some clear differences: compared with the dime/palladium design, the ASE figure has a more curved neck line, lower drapery for the dress, a lower hairline in the rear, a rounder nose, and a more vertical forehead.

Since the palladium coin is based on the Mercury dime and the ASE is based on the Walking Liberty half, what you're really asking seems to be: is the Walking Liberty half based on the Mercury dime or vice versa? Considering they were both designed by the same person at the same time, I suspect the answer is "yes."
Beyond that, a major similarity exists here in the Phrygian cap, which is not a Weinman invention. I actually think that has more to do with the perceived similarity than anything else.

Thanks Spruett001, seems I forgot to take in account for a little fact of the timeline