In viewing authors profile to try to assess their impact I notice that H-index is quite different in Google Scholar and Web of Science (citation report). In Web of Science there is also a search for Author which is marked as "Beta". Which of this reports should I pay more attention to?
Web of Science citations are based on a smaller pool of documents. For one, their collection includes mostly peer-reviewed journal stuff, to the exclusion of theses, preprints and other non-journal sources which can be included by Google.
Because it relies on final journal versions, WoS also excludes citations in intermediate versions that may have been published on arXiv or elsewhere but are removed in the final manuscript. WoS citation counts can also lag actual counts by several weeks, if not months.
On balance, WoS citation counts are subject to less fluctuations than Google’s. I prefer Google because of the breadth of the search, but I would not compare WoS and Google numbers.