I haven't found anything to customize my Wizardlands yet, so I don't know how it works. Just curious about this. I know items don't work across games for obvious reasons of balance, but what about the customized wallpapers and decorations you can get?
Yes, decorations carry over. Also, you get wallpapers when you go down a level, the default is DL1 wallpaper, and when you go down into DL2, you unlock DL2's wallpaper.
I was able to set the wallpaper to the crypt (L2) theme on a new game that hadn't gone there yet, so it appears all the decorations are shared across characters.