Renting after selling frees up your full equity immediately and removes ongoing maintenance and property tax, which suits someone who is not certain where they want to land next or who wants a buffer before committing again. The tradeoff is giving up the stability of ownership and being subject to a landlord's terms.
Buying smaller keeps you in the ownership market and can still release a large share of your equity, especially once seller closing costs of 4 to 6 percent and legal fees of $800 to $1,500 are accounted for on both transactions, but it means going through another purchase, financing and inspection process.
The right choice usually comes down to your timeline and how much certainty you have about your next move, not a general rule. Get your hand-reviewed valuation from Joel Dyck.