If you are trying to observe a relative small voltage across a shunt
resistor and you are finding common mode noise interference induced in
the signal, in what cases would you choose to use something like a
differential to single end amplifier across the shunt VS. a common
You might use both; the CM choke would be used (in conjunction with small value grounding capacitors) to reduce high frequency common mode noise and the lower frequency stuff is handled by the differential amplifier (with appropriately sized-in-value input resistors). The CM choke is to prevent the op-amp having to try and cope with really high-frequency stuff that it is ineffective at dealing with.
Would a diff-amp topology be used for smaller (instrumentation?)
signals in the mV range and a choke for "power supply level" voltages?
A diff amp can be used for any signal levels that are within the design range chosen. Outside the design range of common-mode voltages, the diff amp would become fairly useless.
CM chokes are also used for power supply filtering.