This is a conceptually simple trade-off, although the math would be difficult. Assume that a Federation under Vulcan control would make better decisions but would have more difficulty implementing them (either on a sufficient scale or as effectively) because the strengths that make them better analysts are not the same strengths that make humans charismatic leaders. The Federation might not have as many planets, those planets might not be as willing to implement Vulcan ideas when advocated by Vulcans, etc. Is overall utility higher if Vulcans take the optimal action A% of the time at X% effectiveness or if humans take the optimal action B% of the time at Y% effectiveness? (You would adjust "the optimal action" for the relative strengths of the two species.)

If you believed that AX > BY, you formed the Romulan Empire. If you believed that AX < BY, you joined the Federation. I don't know enough Star Trek lore to say what happens if you end up with different estimates than the rest of your faction (defection, agitation for political change, execution?).