From my experience lately , there needs to be thoughtfulness in communicating the change of methodology abruptly from waterfall to Agile. In projects or organisations heavily dependent on suppliers and vendors change of methodology instead demotivates teh internal team alongwith giving vendors/suppliers a reason to delay their deliveries as it puts in lot of work for impact assesment and contract change etc.
Having several years of experience in running agile projects, there is I think a simple answer your question: do you trust the capabilities of your outsourcing partner or not. With agile/scrum projects only time/material contracts are suitable. Fixed time/fixed scope project etc. are more in line with waterfall projects. So; do you have partners who do you want to participate in your teams or not?