Welcome to the modern era, where there's no actual standard for the brightness of a camera's ISO setting. Yep, really. Two different camera models with the same lens and the same ISO setting are going to look different. There's no physics reason that the full-frame sensor should be brighter.
There's no magic trick here--the sensors are just different, so you're going to have to match them using good old fashioned zebras, histograms, and your eyeballs.