Perhaps the most comprehensive evidence on this question is the Cochrane systematic review (Robinson et al. 2005). The results are summarized by (Forrest and Miller 2004) as:
Searches identified 354 trials, of which 29 met inclusion criteria. These trials involved 2.547 participants who provided data for meta-analysis. Results indicated that for both plaque and gingivitis, all types of power toothbrushes worked as well as manual toothbrushes, however only the rotating oscillating toothbrush consistently provided a statistically significant though modest benefit over manual toothbrushes in reducing plaque (7%) and gingivitis (17%). None of the battery powered toothbrush studies met the inclusion criteria.
A later review comparing different types of powered brushes by (Deacon et al. 2010) concluded:
This review included data from 17 trials with 1369 participants. Brushes with a rotation oscillation action reduced plaque and gingivitis
more than those with a side to side action in the short term. However, the difference was small and its clinical importance unclear.
Due to the low numbers of trials using other types of powered brushes, no other deﬁnitive conclusions can be drawn regarding the
superiority of one type of powered toothbrush over another.
Note: Cochrane systematic reviews are better evidence than simple meta-analyses. They follow a strict protocol that required pre-establishing and registering eligibility criteria, outcomes, interventions, and objectives.
Deacon, Scott A., Anne‐Marie Glenny, Chris Deery, Peter G. Robinson, Mike Heanue, A. Damien Walmsley, and William C. Shaw. "Different powered toothbrushes for plaque control and gingival health." Cochrane Database Syst Rev 18 (2010).
Forrest, J. L., and S. A. Miller. "Manual versus powered toothbrushes: a summary of the Cochrane Oral Health Group's Systematic Review. Part II." Journal of dental hygiene: JDH/American Dental Hygienists' Association 78, no. 2 (2004): 349.
Robinson, P. G., S. A. Deacon, C. Deery, M. Heanue, A. D. Walmsley, H. V. Worthington, A. M. Glenny, and W. C. Shaw. "Manual versus powered toothbrushing for oral health." Cochrane Database Syst Rev 2 (2005).