What is the Extent of the Emergency Authority of the Pilot-in-Command (FAA)?
The scope of the part 91 exception is exactly what it says: deviate from any rule of this part, i.e. part 91. But remember that part 91 applies to all flights anyway; part 121 (or 135 etc.) regulations are in addition to part 91, not instead of them.

But that still means that 91.3(b) doesn't give any authority to deviate from other parts, like 135 or 121 regulations. 14 CFR 135.19(b) is the equivalent authority for part 135 operations:


  In an emergency involving the safety of persons or property, the pilot
  in command may deviate from the rules of this part to the extent
  required to meet that emergency.


Note that the language is again of this part. So in an emergency, the PIC of a part 135 flight can deviate from part 91 rules per 91.3 and from part 135 rules per 135.19.

Part 121 is a little different. 14 CFR 121.557(a) says:


  In an emergency situation that requires immediate decision and action
  the pilot in command may take any action that he considers necessary
  under the circumstances. In such a case he may deviate from prescribed
  operations procedures and methods, weather minimums, and this chapter,
  to the extent required in the interests of safety.


Here, the regulation allows for deviations from any part of this chapter, not this part as in the part 91 and 135 regulations. Chapter I of title 14 is at a higher level: it includes all parts of the FAA's aviation regulations, so under part 121 emergency authority the PIC can deviate from any aviation regulation, not just the ones in part 91 or 135.