What’s the current state of the art in searching for journal articles?
Web of Science is a subscription-based citation database that came out shortly after Google Scholar. I can't compare it to other services such as JSTOR and Galileo (which I have never tried) but at least anecdotally I find it to be better in some respects compared to Google Scholar (better UI and more trustworthy citation counts, at least in my field). However it is subscription-based so whether or not you have access will depend on your employer/institution.
Edit -- There is another citation tool that I feel is criminally underutilized so I feel compelled to promote it. The arXiv has a fantastic browser add-on called the arXiv Bibliographic Explorer which provides detailed information about citations for nearly every article on the arXiv. Even though this is not directly related to your question, I have found it to be an extremely useful tool that not many people know about, so it deserves mention.