If budget is your priority – go for Raspberry Pi Pico.
Easy availability is the first thing, go for Raspberry Pi Pico.
Projects are simpler, RPi Pico wins again but for complex projects and more connections RPi zero takes the Trophy.
Want more memory, Raspberry Pi Zero wins the trophy.
You prefer MicroPython over Raspberry Pi OS then use RPi Pico.
But want to explore new OS for future, go for Raspberry Pi Zero.
Having a Size constraint, RPi Pico is smaller than RPi Zero.