Pubmed has more advanced search capabilities. Google Scholar's main advantage is that it indexes more sources for example it keeps track of the computer science papers published/presented at various conferences. These are not listed at all by pubmed or even ISI. In some fields of comp-sci the conferences carry a bigger weight than journals.
I prefer Pubmed because it gives me PMIDS/PMCIDS which makes it easier to index them later. The old Author/Year indexing is impractical in this day and age.
I also HATE google-scholar's 'Import to EndNote' feature. It occasionally formats them as 'Ancient Manuscripts'. Which is nice for the occasional chuckle (especially when the paper is only 2 years old) but it messes up the meta-data.
PubMed is better for me. Quite a few reasons; You can access it using an EUtilities. For your query you can find related results from other NCBI databases like Genome, Nucleotide, Protein. You can download XML, PMID list and full-text using PMC. PageRank may not be the solution to find out latest publications in research
Personally I think that Google Scholar has as most interesting features the capability to trace gray literature and the user-friendly appearing, while the point of straight of Pubmed are the non redundancy and the pertinence of the results as well as the implementation of the MeSH terms. Often, for quick searches I use just Google Scholar. For deep searches I relay primarily on Pubmed, using Google Scholar as a secondary tool.
Google Scholar is for me the rising star. It did a really great job at identifying my research output. The scope is slightly different I guess, but Google Scholar captures way more research output, including book chapters, (student) project reports, and output in other languages. The latter allow me to identify research groups much earlier (student projects etc) much earlier than with other research output.
I tend to use both in different ways. I use Google Scholar to interface with my library's databases and to follow reverse citations and related articles. When I want to capture citation information with Zotero I'll generally use Google Scholar's link to the Pubmed version, as it is generally much cleaner (including journal abbreviation, DOI, etc.). However, if I'm in the middle of writing I'll often just copy and paste Google Scholar's BibTeX output into my .bib file.
The main problem I find with google scholar is that it doesnt base the results that it shows on anything other than if the 'paper' is formatted like a 'paper'. Since finding this out I've spent a lot more time checking out the credibility of the journals that my sources come from.
Still doesnt stop me using it though.