Since Snow is still a child (14 years old), definitely Rapunzel.

Snow White took charge in the cottage with the dwarfs she cooked for them took care of the house, and she played with them but when it got late she knew when it was time to sleep, if it was Rapunzel she would have stayed up all night playing with them.

I wouldn't call them childish, more childlike.

i don't see how Snow white is childish, actually. she looks more mature and responsible than most of the princesses

she acts like a 10 year old, and she's 18...

She has been sheltered her whole life so she has remained more naive the the other Princesses...Snow White most likely saw a lot of bad things happen while living with the Evil Queen and had to mature quicker for her age and she had to basically take care of her self after her father died....Rapunzel was taken of care of by Gothel and was kept in the dark about a lot of things....

Snow White's actually pretty mature when you think about it.
Rapunzel's very naive and childish, and acts too young. She seems more like a 14 year old than Snow does.

I don't think Snow White is naive at all, actually quite mature. Rapunzel on the other hand is very naive especially in the beginning of the movie

I have to disagree with the opinion of majority. Rapunzel's "childishness" is something that was the result of emotional manipulation and years of isolation and oppression caused by her passive aggressive mother figure who brainwashed her into believing that she actually took care of her and basically held her hostage in a tower for her own good and safekeeping, telling her all those horrible stories about the outside world, people in it and making Rapunzel insecure and sheltered, making her believe that the life outside the tower was too scary, complecated and dangerous and that Rapunzel herself was too naive and silly to survive out there. Yet still Rapunzel took chance to follow her heart and fight for her freedom and when she entered the world for the first time ever in 18 years she actually handled herself pretty maturely and as a civil person. She managed to find a common ground with thugs and bandits, she overran the army of the guards, she formed a strong bond with Flynn and finally she standed up for herself to Gothel in the end, being ready to fight untill the end. Snow White on the other hand knew that her step mother was evil - not just oppressive but actually evil - and she forced Snow to work as a servant yet Snow never attempted to get away from her or to fight for her freedom. When prince comes Snow barely knows how to actually react to his presense and she doesn't even have a conversation with him like Rapunzel with Flynn. Snow is completely naive and unaware of anything regarding life and when she gets to face this life, unlike Rapunzel who manages to handle herself pretty well and in the end stands up to her villian, the only option Snow manages to find for herself is convincing the dwarves to let her stay in their house while she will be cooking and cleaning up. Then she lets a stranger into her house even though not only she knew that the Evil Queen was after her, but there was an attempt on her life already prior to it when the Queen ordered Snow to be killed by Huntsman, using the other person to fulfill her plan, and Snow should have taken all of it in consideration yet she ends up eating the apple from a total stranger. Snow comes off much more childish than Rapunzel imo, but to be fair, she was actually younger than Rapunzel so it's understandable.

genuinely childish, snow white.

I think Snow White is somehow act more mature than her age.