[Avodah] Kosel vs shul in Old City

[kennethgmiller at juno.com]

R' Daniel Eidensohn wrote:
> I davened mincha today in the Ramban's shul in the Old City.
> Someone objected and said that I should have prayed at the
> Kosel since it has greater sanctity.

What is the nature of that extra kedusha? Both locations are outside the Beis Hamikdash. Both locations are outside Har Habayis.

I am under the impression that Both locations are within the most ancient walls (e.g., are equal are regards Lulav on Chol Hamoed, and Maaser Sheni), but maybe I'm wrong?

Akiva Miller