When peer reviewers are public/open, are they less likely to be critical of a manuscript?
I have a similar history of reviewing papers at around eight years, though in the fields of engineering and robotics. Between the official reviews for journals or conferences (which are almost all single blind and in rare cases double blind) and informal reviews for colleagues, I would say I differ only in level of tactfulness.

The stakes in the official review process, however, are higher and I would not agree to review if my name was to be released.  I’ve rejected papers based on lack of contribution (to the extent where there were missing citations of seminal papers or even their own previous work to make the current paper look more significant) as well as lack of fundamental understanding of the involved system or experimental processes.  These types of issues are not things that can be easily fixed and the review becomes more of a statement of ‘start over’ with the associated large investment of time, money, and/or resources.

Peer review requires an already rather generous donation of time by those who participate. In an open peer review there is additionally a very real fear of retribution, which only the well-established can easily ignore.  My personal experience follows the results of the previously mentioned van Rooyen et al. – review quality in an open process stays approximately the same, but the number of willing reviewers decreases, potentially drastically.  The open review process certainly has some value, but I don’t consider it to be widely practically implementable with the current reviewer arrangement.