The time screen has more animation, though.
If you don't care about your Tamagotchi's growth, then pause it.
Personally, I care more about my Tamagotchi's growth than the batteries, so whenever I can't take care of it I just put it to sleep.
Either way you choose, you'll still lose batteries eventually. If you don't want to let the batteries run out at all, take the batteries out.
If you still have the battery tab that came with the Tamagotchi that you needed to pull out to activate it, slip it back in.
This halts the Tamagotchi's growth completely, obviously.