There is NO downgrade, the two parts are different. FAR 125 is just FAR 91 operation with some added requirements, but nothing like 121. 121 = Commercial operation; 125 = private operation of aircraft with a payload of 6,000# or more OR an aircraft with 20 or more certified passenger seats. A SAAB 2000 is Part 125 as can be a CRJ. Operators have configured BBJs to meet 135 specs, that is designed in 19 pax seats or changed the ZFW to limit payload to 5,999#.
From 125 Applicability:
a) Except as provided in paragraphs (b), (c) and (d) of this section, this part prescribes rules governing the operations of U.S.-registered civil airplanes which have a seating configuration of 20 or more passengers or a maximum payload capacity of 6,000 pounds or more when common carriage is not involved.
(b) The rules of this part do not apply to the operations of airplanes specified in paragraph (a) of this section, when—
(1) They are required to be operated under part 121, 129, 135, or 137 of this chapter;
GF