A part-time employee status (vs contractor) generally comes with loss of control over one's working hours, 30-hour weekly caps (to avoid the ACA penalty), and compensation setup that involves some kind of (likely minimum) wage + bonus instead of straight-up 1099 income.
Most of the gig economy (Uber, TaskRabbit, PostMates) is built around flexibility of hours, and freedom to not only accept a gig, but to refuse one (which you lose if you're in an employer-employee relationship and the boss is simply assigning it to you).