The Traveler showed signs of physical stress while attempting to get Enterprise home. And the crew were ordered to think happy thoughts about him to help him do this. The Q never seem to tire when using their powers, which seem to require no preparation or hocus pocus mumbo jumbo.
It also appears that The Traveler lives up to his moniker, with his primary power being the ability to travel great distances (and even between dimensions). No doubt it was simply the sheer amount of material and/or people he was having to move that was draining his abilities.
The Q powers are much more varied.