James Battista has a piece (gated) in the most recent State Politics and Policy Quarterly examining formal and perceptual power among leaders in the state legislatures. That is, he compares an index of actual formal powers of statehouse speakers (control of the legislative agenda, appointing committee chairs, etc.) with the results of a survey of legislators about how powerful they believe those speakers to be. The result? Essentially no correlation between the two.
I regret that Battista's analysis excluded Nebraska, as I'm curious where that state would show up in the survey.