I think they kept a pretty fair balance of stories for all the characters over the course of the show, but the movies focused on Picard and Data to an unhealthy degree given that neither of those characters was compelling in the way that Kirk and Spock were, and even the TOS movies established more of an ensemble feel than the TNG films.
Agreed on these points!
I don't think there were too many characters, but, one of the drawbacks of having a larger cast was the fact that it became very difficult to highlight all the characters equally, although it was clear that the writers tried to do that. This resulted in a lot of character-oriented loose ends at the end of the seventh season that were completely unaddressed by the movies.
The strength of TOS was its ensemble cast, although a handful of the characters were featured more prominently than others. TNG, I think, had a similar strength on TV, but that strength was very much downplayed in the films. I think that First Contact was probably the only film that, by distributing the main characters between two plot scenarios, achieved some level of character equality.