HiFi chips are definitely overkill. In the zendrive design the clipping is done with the mosfets and schottky diodes in the opamp feedback loop. Chips like the TL072 already have good enough noise specs and slow rate for these applications.
The only reason why I can think you might want to try different opamps, is :
- to reduce power consumption (by using less ideal opamps, that may suit the specific functionality in the circuit),
- to test different opamp rail clipping behaviour (only makes sense when the opamp is actually clipping in the design. Here you can try using chips with different internal output topologies, like rail-to-rail output),
- or to use chips limitations as part of the sound itself (like all the RAT pedals that use LM308 ICs for their low slew rate).
There are some reports of biasing differences when using bipolar input opamps vs fet input opamps. I've never experienced it myself.