I would like to hear the opinion of researchers from different parts of the world. In Brazil (in general) the index "h" of the web of science is considered more robust as an indicator of "quality".
Generally, the Web of Science offers a more comprehensive coverage. The inclusion in JCR is a somewhat rigorous process, and for these reasons it is considered a more robust tool. However, your question is "the best indicator of production QUALITY" - but citations are not are not a reliable indicator of an article's or journal's overall quality. These are different things. Incompetent administrators use and abuse it all the time, but this is just wrong. Each paper should be assessed based on its own merit, and citations are just one of the many factors.
the Web of Science, Scopus and Google Scholar respectively. ... Citation Index Citation Count Citation Database Technology Indicator Hirsch Index based on paper quality..
I agree with Alexander Serenko - the Hirsch (H) index is not the solely indicator and should be used for what it is desined to represent. As to comparison between WoS, Scholar and Scopus - H works exactly the same way, just the database/selection of papers its applied to is different. WoS uses only their "qualified journals", Scopus their journals, Scholar practically everything Google can find and classify as a scientific output...
Practically speaking, the preferred database should be the one which will broadly cover all the scientific platforms/sources where any research/review article has been cited. In this aspect, Google Scholar served the purpose. Inclusion in Web of Science and Scopus database is very rigorous, and hence, their database is very small as compared to Google Scholar. If we look at the citations covered by google scholar, it is basically covering all the journals or books who has ISSN or ISBN number. Frankly speaking, that's not wrong even.
In India, the most used H-Index is the one obtained from Google Scholar.