I think common law is better for a healthy democracy.
It seems to me that the only countries that use common law (that is, basically former British colonies) are all fairly lacking in democratic standards. There is a wide variation among Civil Law countries, but they include all of Northern Europe, which strikes me as a far better model to aspire to.
I don't think common law is necessarily better for fostering democratic institutions; I mean that I think it's better for countries where democratic institutions are already well-established, whereas with newer democracies or mixed regimes it's probably best to have the clarity and systematization that civil law provides. This is a prescriptive hunch (and not really much more than a hunch), and not necessarily connected to the systems that various countries actually have.