Not enough to matter really .. the Rim is just a really Big Disc.

There are Hydraulic Rim brakes Too .. Magura Of Germany has been making them for decades. [I like Mine]

they keep redesigning the MTB Disc Brakes , but the design of their HS33 rim brake has stood the test of time.

Disc brakes work with a damaged rim, since you dont ride in the rain their wet braking benefit is Moot.

Like the Hydraulic discs in your car the hydraulics compensate for pad wear reduced thickness

with a cable brake, the adjuster is You , or the occasional check up at your Local Bike shop.