I personally don’t think there is a rule. I don’t wear a watch and bracelet on the same wrist as I don’t like the sound they make hitting each other and the inevitable scratches.
The watches that I wear alone are my watches with exceptional faces. I have a hand painted face Patek Philippe and a Hermès millefiori face by Saint Louis. The two are miniature art pieces, so I prefer them alone.
All my other watches I tend to wear with a statement bracelet on the other wrist. I like for the metals to be the same tone unless the bezel of the watch is pave with diamonds. All my watches have relatively small cases and are all on straps, so they rarely clash.
Now, this may just be me, but I don’t like wearing a ring larger than the watch case on the same hand. This is rarely an issue except when I wear my pave faubourg watch.