I'm on the eCommerce team at Petco corporate, so Chewy is my biggest competitor.
Chewy is better for a one time purchase that you need quickly, as their shipping is generally faster, especially to remote areas. They are 2 days and we're closer to 3.5 click to delivery, but improving.
Chewy is cheaper on a lot of items too, although we just did a big permanent price cut on food to realign.
Petco has a better customer rewards program and way better privately owned brands.
They both have repeat delivery. You will also see buy online/pick up in store rolled out at Petco soon.
Petco has free ship no minimum on Fridays, and all holiday season.
Hope that helps.