Who are "we" ?
It used to be that Falcons, Lears, etc. fit under Part 135, but in the last ten years that has changed, as it has for 19 and 30 seat regional aircraft. When I worked for a " commuter " airline we were Part 135 then I went to a major which is obviously Part 121, and then to a Non-Sched which was Part 121 Supplemental.
The big difference between 121 and 121 supplemental where I was concerned was flight and duty time limitations. We also picked up some scheduled runs and had to be real careful to be legal for those versus our normal flying. The 121 rules were much more restricitve than 121 supplemental. I remember one key word missing from the supplemental regs was " consecutive ", as in 8 hours of rest or 8 consecutive hours of rest. We had a lot of fun with that one, not.
Typhoonpilot