the much more active/much the more active

[joham]

Of the two students, Bob is the much more active/much the more active in politics.

Are the two phrases fine for the sentence?

Thank you in advance.

[joham]

I read in Webster's Usage the two constructions and wonder if they are interchangeable:

acceptance, acceptation
...
Acceptance is much the more frequent word.

stanch, staunch
...
Stanch is the much more common spelling of the verb:
.. . the icy cold .. . had stanched the flow of blood
—Brock Brower, Holiday, February 1966

Thank you again.

[Raymott]

Of the two students, Bob is the much more active/much the more active in politics.

Are the two phrases fine for the sentence?

Thank you in advance.

Yes, they are both correct.