I'm actually confused by that analogy, so I apologize in advance.
So far I've gleaned the pro's and con's of both.
Commanding Voice is cheap, Drain free, and works on multiple targets, just like emsquared said. Con's include the resistance built up to those already affected by it within the last 24 hours, and also the 5 words/must speak target's language/must be heard limitations. Not a subtle power all the time.
Influence has no resistances(unless your target is asked to commit an action they would not do under normal circumstances, like suicide, or taking lethal action against a loved one), does not have the requirements CV needs to be used at all, and has as long a range as your senses go for. Con's include being able to counterspelled, Drain(though relatively minor), and wards blocking it.
Both seem good to have, with CV simple things, while the heavier stuff is left to Influence.
CV seems to be the Charm Person to Influence's Dominate Person.
Addendum: Influence works on critters(non-sapient), whereas CV does not.