https://furniture.cort.com/storefront/
Just browsing through here suggest they offer more flexible renting periods, (starting at 1 month vs Feather's 3 month requirement), and a website ui and design that looks fairly modern and easy to navigate.
Cort seems to have higher prices for similar goods (only looked at sofa's), but competing against a much larger corporation on price seems to be a bit of a bad business strategy. In the long run I would guess that if feather seemed like a threat, Cort would simply undercut their pricing in the competing market. I don't see what feather has to offer other than the YC branding and a younger target market.