Volodymyr - it really depends on what you what and how you want the h-index to represent you. Most will want the 'maximum' value. Google Scholar tends to be the most generous that you have mentioned - with WoS the most conservative. That tends to put Scopus in the middle. What I suggest is certainly the case with my academic profile. Check it out if you are not sure.
until now in my country SCOPUS is still a concern. Nevertheless, it looks like the rules will be a change. All journals will be re-weighted and evaluated which has a better academic weight
In Google Scholar its very easy to fabricate a high value of h-index by self citations in predatory journals. There is no way to filter such fake citations.
Scopus covers both: best quality journals and conferrence series. It spoiles slightly its creditability (as Witold Bogusz mentioned). However, there are some options in Scopus like: "exclude citations of all authors" in "cited reference search" menu that help to measure real external impact. WoS also provides 2 values of h-index (with and without self citations) but is less generous in abstracting and indexing of conference papers (see Dean Whitehead comment).
Personally, whenever I check somebody's real impact, I use Scopus and "cited by" in "view in search results format". You may exclude author's affiliation (meaning: self citations and citations from home institution).
I agree with Jaroslaw Rybak comment, fabricating a high value of h-index by self citations in predatory journals is a real problem, that there is no way to filter such fake citations.
The real answer to this question is to discover what YOUR school considers to be valid for purposes of promotion and tenure. If your school will accept Google Scholar, by all means use Google Scholar. If the promoting authorities within your school expect a different index, use the one they prefer.
It depends on what you want from the h-index value. As many colleagues mentioned above, the three databases you mentioned use different criteria to measure the h-index. The question is: WHAT IS THE REASON YOU CHECK THE H-VALUE FOR? If it is for promotion or grants, then check what the institution you deal with and follow what is best for your goal.
If it is for your own or to check someone's real reputation, then I would trust WoS the most.
No h index is of any value except for idle curiosity. Hirsch, the inventor, agrees with this. It's an amusing mathematical curiosity, and should be treated as such
1. Google Scholar : Widespread coverage; accumulates large number of citations inclusive of citations from almost every publication, even lesser known ones, resulting in higher higher h-index.
2. Scopus : filtered coverage; largest multidisciplinary database having a standard protocol, only includes publications that follow certain Elsevier-Scopus formulated guidelines; naturally we see a truncated h-index.
3. Web of Science: Most filtered multidisciplinary database, only considers publications of very high repute; collects citations from among the core WoS indexed journals only; consequently h-index is very low but of high potentiality.
Most universities will ask h-index calculated from Web of Science or Scopus. I do not think Google Scholar is useful, many citations are from non-peer reviewed articles, and others
Really, both of them are essential, and it is better to say that, in both cases, h-index must be equal in magnitude, but there is a difference in its values which is depending on the database for each academic site.
Presentation Journal Impact Factors, Researcher h-index, How to improve r...
Ask your VC Dean of research which databases you may use to calculate your h-index. Most journals recommend the Web of Science. However, others recommend Scopus or Google Scholar. You need to find out.