I think objects with a strong emotional attachment to them were brought over by the curse.
We have:
The chipped cup- Rumple’s memory of Belle.
Emma’s baby mobile- Snow and Charming got it for their daughter who they had to send away the moment she was born.
Hansel and Gretel’s dad’s compass- Te last thing he gave to them before he disappeared.
Gepetto’s puppet parents- Jiminy felt guilt over what happened to Gepetto’s parents because of him.
Red’s cloak- Red had to wear it to stop herself from transforming into a wolf and hurting someone.
Snow’s coffin- When Snow was believed to be dead, she was put into the coffin until Charming awoke her with true love’s kiss.
Interestingly enough, none of these objects have a positive emotion attached to them but represent grief, loss, fear and guilt.
All magic comes with a price!
Keeper of Felix