Except Grammarly can only be more trustworthy than Google and Grammarly claims that nothing is stored after analysis.
Considering how Grammarly would face a customer exodus overnight if they had a data scandal involving the text typed by their users, it seems a fairly safe bet that they have solid privacy controls in place. Anyone paying $120+ a year for Grammarly most likely has writing as a core component of their profession, and would run for the hills if the security of their content was compromised.