Photo stream only keeps photos for up to 30 days. It's used to sync photos from one device to another and the 30 days gives you time to receive the photos and move them to a permanent album on the receiving device/computer. Photo stream should not be used to store/archive photos. For that you should always sync photos to a computer to archive them.
On the other hand, if you made backups of the old device to itunes or icloud and had backing up the camera roll turned on, then those photos would sync back to a new device if you perform a restore of the backup to the new device.
Restoring to a device:
Go to Settings>General>Reset and tap Erase All Content and Settings. This will erase your device. Then you will go through the setup screens again as you did when your device was new, and when given the option, select Restore from iCloud Backup.
This link gives another overview of backup and restore:
HOWEVER... you may run into a snag, namely when the newly restored data is downloaded, an automatic icloud sync may occur that will wipe out any Apple data (contacts, calendars, etc) that was restored. If you have such an issue, read the following that describes restoring contacts. The info will also pertain to other Apple data.