The verdict
If you take applications, registrations or intake from outside, and the form should look like your brand, pick Fillout. If several people inside the team run the same procedure and you need proof of each step, pick Process Street.
A small team could use both, with Fillout collecting the request and Process Street running the work. For a solo operator with a few checklists, Process Street may be more than you need. It has no free plan, only a trial on Pro, while Fillout has a free plan.