You cannot go wrong choosing any of the tools, but it helps if you take a few things into consideration before starting. Remember that you can switch between the tools, it just becomes less convenient the longer you use a tool and the more file attachments you collect.
Reasons to choose Zotero:
Your research content is diverse: It is the easiest method to gather citation records for non-PDF and PDF content. Zotero's single-click capture works with more databases, catalogs, and websites than Mendeley's Web Importer. You can also enable the retrieval of PDF metadata, which allows you to create citation records just from dragging a PDF into Zotero. Zotero is open source and cannot be acquired by a company.
Reasons to choose Mendeley:
Your research content is primarily contained in PDF files: Mendeley has an integrated PDF viewer and can create citation records just from importing a PDF file. Mendeley.org has the strongest website and community platform.
Reasons to choose EndNote:
Zotero and Mendeley are relatively young tools when compared to EndNote. EndNote X6 offers some advanced features that might be necessary for your discipline and work flow. However EndNote X6 is not free and can be purchased with an educational discount through the Washington University Campus Store or E-Academy. Currently, EndNote for WUSTL students for $24 : https://sts.wustl.edu/sas-mathematica-and-endnote-for-students/.