Hotline studied California election returns in 1998 and 2000, and determined that the California top-two open primary is likely to injure Democrats, relative to Republicans. See a description here.
In 1998 and 2000, California used a blanket primary. All candidates for all partisan office appeared on the same primary ballot, and all voters used that primary ballot. The top vote-getter from the ranks of each party advanced to the November election. Therefore, the blanket primary did not injure either major party relative to the other. But the data from that period shows that in the top-two open primary now in effect, Republicans gain a significant advantage over Democrats, because Republican voter turnout is consistently higher in primaries than Democratic primary turnout. That means, sometimes, no Democrat ends up on the November ballot, even in races in which Democrats might have been able to win in November, if only they had a candidate on the ballot. Thanks to Rob Richie for the link.