Is there any real world difference in upgrading TL071 to OPA314?
Chances are low that you will notice any affect by changing the opamp, assuming the two are even compatible in the first place.  You didn't provide links to datasheets, so I haven't checked.

A TL07x opamp, when used properly, can make a nice audio amplifier.  It can also make a mess, as can any opamp, when used improperly.

Gain is a function of the circuit around the opamp, and output voltage swing largely a function of the circuit.  The TL07x series do have rather high power rail headroom requirements, but presumably that was taken into account in the design of the circuit.  The opamp, unless it's really bad, should have little effect on "sound quality", whatever that actually is anyway.

In general, just replacing a part in a competently designed circuit with something that supposedly has higher specs is not a good idea.  You don't know what the design considerations were, and don't know exactly how the part is used.

If you don't understand a circuit, don't mess with it.