Parallelling is something derived from the design of power stages, where one might have multiple power transistors or power tuibes in parallel so as to be able to deliver more current to the speakers (and more wattage as a result). It also is regularly used for things like headphone amps where the outputs of two op-amps are paralleled to provide enough power/current to the headphones to be audible.
The thing is that when those sorts of elements are paralleled, interaction between their device inputs is not an issue because of how they are used. Although one CAN simply piggyback op-amps (of the same type/category - you can't piggyback a dual on top of a single) by soldering their pins together, and I've done it with interesting results, one of the problems or byproducts is that the input impedances of the devices are now placed in parallel. This didn't dawn on me at first when I paralleled a pair of NE5534s in my Distortion+ and noticed a certain "timidness" to the high end (and maybe that is what rockgardenlove means by "smoother"). Then, someone noted here the other day that the input impedance of the Signetics NE553x series op-amps was pretty low, and I realized that placing two such low-impedance inputs in parallel was unlikely to be a great idea for a circuit intended for a single op-amp to serve as input and output stage - often as the first thing the guitar sees.
Having said that, placing a high-current-delivery/low-input-impedance op-amp in parallel with a lower-current-delivery/high-input-impedance opamp should give the best of both worlds.