I'm still learning ECC, but considering that the X and Y coordinate of a bitcoin public key are both 256 bits resulting from point addition of 256-bit Generator Point, isn't a bitcoin public key technically 256 bit?

Reference: http://www.royalforkblog.com/2014/07/31/address-gen/

The only caveat I remember, is that even though a given ECC operates in 256-bit space, it has only the equivalent of 128-bits symmetric (e.g. AES) security.

The caveat explained by DeathAndTaxes here: https://bitcointalk.org/index.php?topic=1007619.msg10936084#msg10936084