Photo Stream is for photos only; it does not upload and sync videos across devices. Also, only photos taken after Photo Stream is enabled are uploaded. Photos taken prior to enabling Photo Stream are not.
In order to transfer videos from one device to the other you need to import them to your computer as described here: http://support.apple.com/kb/HT4083, then sync them to your other device by select them on the Movies tab of your iTunes sync settings and syncing. The same can be done for older photos not in Photo Stream: you can import them to your computer, then put them in a folder and sync them to the other device by selecting to do so on the Photos tab of your iTune sync settings and syncing.
Forgot to mention.... Also, backing up to iCloud only backs up your photos and videos as part of the overall device backup. The photos and videos cannot be viewed or accessed separately. They can only be restored to the device (if necessary) as part of restoring all settings and data contained in the backup.
You're welcome, but to clarify, iCloud is designed to make your photos and other synced data available and consistent across devices. For example, if you turn on photo stream and then take a picture on one device, when you close the camera, connect to wifi and have at least 30% battery charge left, the photo will upload to your photo stream. Once uploaded, it will be streamed to any other device that is connected to the same iCloud account with photo stream also enabled (appearing in the photo stream album). But it does have limitations, such as only keeping a maximum of 1000 photos for up to 30 days, and it doesn't include videos. In other words, photo stream is designed as temporary storage until you save the photo on your device or computer.
Another example is contacts and calendars. If you add a contact or calendar event to your iCloud contacts or calendar on one device, it will be uploaded to iCloud and synced to all other devices connected to the same iCloud account. Conversly, if you delete a contact or calendar event, it will be deleted from all devices connected to the account.
It also provides a way to back up your devices automatically every 24 hours, and the backup includes your photos and videos.
Hopefully that clarifies things a bit.