I have tried both the headphone out and LR out options for my Tonex pedal. In my opinion the headphone out seems to be far superior to the LR outputs. I run my Tonex out to a SA Collider to handle delay and reverb and there is a noticeable "hifi" nature to the headphone out versus the LR outs. I use two 6 inch instrument cables to connect the Tonex LR out to the Collider inputs. When using the headphone out, I utilize a 3 foot Insert or Y-cable (1/4" TRS to two 1/4" TS connectors). The Collider output goes into a stereo channel of my Mackie Mix12FX before output to my studio monitors.
Is it because the direct outs are unbalanced? Is it because the headphone out has an amplifier? I would assume the headphone out circuitry would color the sound unfavorably. Do both outputs receive the same processed signal or is additional processing done to the headphone output?