I was told anecdotally by Arizona politicians that the state's Clean Elections law helps empower more extreme candidates and now political scientists Seth Masket and Michael Miller have the research (PDF) which backs that conclusion up. Looking at Arizona and Maine they find that "clean" funded candidates "were more ideologically extreme relative to their districts and parties than traditionally-funded legislators were." Their hypothesis:
These findings suggest that it's the more ideologically extreme candidates who take advantage of clean funding to run for office. Under the traditional funding system, party donors function as gate-keepers, reducing the power of extreme candidates by channelling money away from them. Take away the gate-keepers, and it's the extremists who break through, contributing to the polarization of the legislature.
That's interesting stuff, though I do wonder how far the result really generalizes. There's a great deal of diversity in American state legislatures, and though Arizona and Maine are very different places they are similar in having very amateur state legislatures. It's not obvious to me that campaign finance changes would have the exact same impact on a more professionalized legislature like New York or California.