No one database can cover the literature for any topic. For medical topics, a combination of PubMed (or other search of PubMed data) plus Embase, Web of Science, and Google Scholar has been shown to provide adequate recall (Syst Rev. 2017;6(1):245). For topics that reach beyond the biomedicine, other databases need to be considered.
These database can be an effective complement to your search. They can be essential in their specialized topic areas.
Truely unbiased searches look for unpublished literature in a number of places, included meeting abstracts, white papers, clinical trial registries, and searching by hand.
Identifying sources for grey literature and being sure you've done enough is a challenge. The Canadian Agency for Drugs and Technologies in Health (CADTH) feels your pain and has produced a checklist that might help guide your grey research. The Grey Matters checklist provides an organized source of health technology assessment sites, regulatory agencies, trial registries, and other databases in a form that can help ensure the completeness of you search.
When you search Cochrane Library/Trials, you will see results from both ClinicalTrials.gov and ICTRP.
More information about trial registries and solving the problems associated with searching them is available through this site:
Medical and health-related trials registers and research registers
which is maintained by Julie Glanville and Carol Lefebvre and hosted by the York Health Economics Health Consortium.