Hey there, malene114!
We appreciate you reaching out on Apple Support Communities. From your post, it looks like you’re trying to restore data from one device to another, and you’re unable to due to storage. We’d be happy to help out!
Just to confirm, do both devices have the same storage amount? You can check in Settings > General > About. Depending on the type of backup you’re trying to restore, there may be more data than you have available on your new device. To see how much data is contained in the backup and how to manage that, check out: Locate backups of your iPhone, iPad, and iPod touch - Apple Support
Cheers!