As one who got his mechanical skills helping with the hangar work as part of the payment for his flight time, I'd say avionics will be much more helpful in the cockpit as a pilot.
I teach avionics and aircraft systems and it was the avionics experience that got me most of my jobs after I quit flying.
I agree that a guy that can help out in the hangar is a valuable assett but if you're looking for a deeper understanding of why something happened when you threw a switch or lever avionics is the discipline that ties the most systems together.