I remember hearing Garret Wang saying in an interview that Berman didn't have a clue what was going on on VOY's sets. He would drop in maybe once a week (if at all), boss people around for a while and then go about his business (which, apparently, was everything except Star Trek at that time).
And yeah, Wang also openly called him an idiot.
Honestly, this says a lot to me about the level of company interference.
According to DS9 fans (I believe based on a Moore quote?), their show is better because Berman ignored it in favor of Voyager. According to a Voyager actor, Berman ignored Voyager.
So, basically, he either had no impact on either show or, quite likely, equal impact. The biggest difference, then, would not be Berman, but UPN in impacting creative decisions on Voyager.