Yeah, a game with both is the way to go. I think an overarching story keeps me more interested in general, and I definitely like that approach better on TV series, but for a game I also appreciate the smaller character-driven stories.

It's tough to compare the two because usually if a game does one right, it does both right, but here's an example from the top of my head that specialize in each of these:

Character-driven: Final Fantasy XIII
Overarching: Suikoden II

If I had to choose between the two I would pick SII's story but that might be more because SII was the better game. However, I do think its focus on the larger story was a factor in making it so good. For FFXIII, it definitely had a character focus but a lot of it feel flat since the overarching story was so poorly written.

However, a game like Chrono Trigger or FFVI that has both going on is all around excellent.