while this maybe one of the more difficult ways to move everything, it should work fine as long as they are both on the same version of steamOS.

You might have issues if you use a pre-3.5 build on OLED or not boot properly

I would recommend neither. Just copy over USB or network the home folder, if you left the OS partition as read only than all the steam stuff should transfer easily. Non-steam programs like lutris or ProtonGE or emulators might need to be reinstalled but their settings should all transfer. The new deck is fine with opening & closing but the LCD decks never go back together (big improvement in how they are screwed together)

while this maybe one of the more difficult ways to move everything, it should work fine as long as they are both on the same version of steamOS.

You might have issues if you use a pre-3.5 build on OLED or not boot properly