With hindsight it's easy to choose which side, but I think that at the time you would have chosen based on you financial situation.

Much like elections today, rich people would tend to favour the status quo (republicans), as that's the system that has made or kept them rich. The poor would side with whomever offered them the easiest life (bread and circuses), with the fewest wars and other of life's hardships. The middle classes who felt that they could do better with more opportunity would be most likely to favour change, and that's where Caesar got a lot of his support. Of course, having an army that owes it livelihood and pension hopes to you helps, but most good generals since Marius had one of these.