Thelwall*, Klitkou, Verbeek, Stuart and Vincent (2010) set out to find in which fields webometrics is most effective. The result is quite a long paper, that I'm going to be very general about its conclusions. As expected, webometrics doesn't have the same effectiveness in every field. It is at its best with emerging and/or "hot" fields. That is because web publication is easier and faster than publication in traditional scientific outlets, and researchers can publish ongoing results with little delay.
In some disciplines plenty of their products aren't regularly published in journals (social sciences, humanities, applied fields, etc.) and therefore aren't as well-covered by bibliometrical databases as disciplines with a journal-publishing culture. Bibliometrics is also bound to have a poor coverage of multidisciplinary fields, because their outputs are published in various outlets and are often cited in different manners.
In general, webometrics analysis gives better results in fields with standards and/or norms for web publishing, but the results might not be reliable in fields where a small number of research groups and their projects (databases, web portals and so on) have a disproportional web presence.
Collaborations are often better caught in webometric analysis, since not all collaborative works have "official" outputs.
Webometrics works better for smaller fields. It's harder to get a complete picture of large fields with current methods.
Last but not least: webometric analysis is usually faster and cheaper than bibliometric one.
Thelwall and his colleagues concluded that "whilst webometrics is still inferior to bibliometrics for most purposes it seems that it has advantages for some types of field, particularly new, small fields, and can deliver policy-relevant (process) indicators to promote effective collaboration and communication," (in short: use with caution).
Appropriate disclosure: Prof. Thelwall is one of my dissertation advisors . My favorite from his long list of achievements is that he managed to publish a serious research paper including a YouTube cat video.
Thelwall, M., Klitkou, A., Verbeek, A., Stuart, D., & Vincent, C. (2010). Policy-relevant Webometrics for individual scientific fields Journal of the American Society for Information Science and Technology, 61 (7), 1464-1475 DOI: 10.1002/asi.21345