Not having subscription access to Zentralblatt, I won't try to comment on its merits. Leaving that aside,
MathSciNet is certainly the most comprehensive database of published work in mathematics (and to some extent the closely related areas of mathematical physics, etc.). It's constructed and maintained by a substantial paid staff of professional mathematicians and technicians, with no advertising revenue. Though AMS is a nonprofit organization and MathSciNet is partly subsidized from voluntary membership dues, there is no free lunch. For some time now they've compensated reviewers, who used to work for free, with 8 dollars worth of AMS credits for each review written; it's a token payment but eats into AMS book revenues.
Availability to people outside the North American system of colleges and universities which pay for the service is always problematic; there are frequent arguments in the AMS Council about how to subsidize MathSciNet as well as journals and books for developing countries. Anyone in doubt about the complexity of AMS finances should try to chat with the incoming AMS president Eric Friedlander, who has long experience as a trustee.
Having said that, I'm one of the lucky people who (so far) have MathSciNet access
and can use my university system password even at home. Whether our financially stressed library continues the arrangement is an open question, since they have to cancel hundreds of journal subscriptions every year even in stable economic times.
On the plus side, MathSciNet has developed its search capabilities even though there is usually too little access to the text of articles or books to search that far. And for a couple of decades the ability to list references in a given paper and citations to the paper in reviews or other papers has grown rapidly. Another very useful feature is the author profile (even for the elusive et al.), with lists of all published work and links when possible to co-authors, math genealogy.
Also on the plus side is the professionalism of the staff and the attempt to keep all data precise, even the troublesome identification of authors by sometimes variable or duplicated names (notable for Chinese authors).
For me Google Scholar is a back-up source of limited use (and limited trustworthiness), which often has the defect of giving too much information in a time-wasting format. But it's definitely free of charge and will contain even more information if publishers can be persuaded to hand over all content to them
(presumably in exchange for advertising space or priority listing or even old-fashioned cash).