Photos and videos in the iPhone's Camera Roll are just one part of the iPhone's backup.
http://support.apple.com/kb/ht4946
- Camera Roll (photos, screenshots, images saved, and videos taken)
For devices without a camera, Camera Roll is called Saved Photos.
- Contacts* and Contact Favorites (regularly sync your contacts to a computer or cloud service, such as iCloud, to back them up)
- Calendar accounts and subscribed calendars
- Calendar events
- Safari bookmarks, cookies, history, offline data, and currently open pages
- Autofill for webpages
- Offline web application cache/database
- Notes
- Mail accounts (mail messages aren't backed up)
- Microsoft Exchange account configurations
- Call history
- Messages (iMessage and carrier SMS or MMS pictures and videos)
- Voicemail token (This isn't the voicemail password, but is used for validation when connecting. This is only restored to a phone with the same phone number on the SIM card)
- Voice memos
- Network settings (saved Wi-Fi hotspots, VPN settings, network preferences)
- Keychain (includes email account passwords, Wi-Fi passwords, and passwords you enter into websites and some applications)
If you encrypt the backup, you can transfer the keychain information to the new device. With an unencrypted backup, you can restore the keychain only to the same iOS device. If you're restoring to a new device with an unencrypted backup, you need to enter these passwords again.
- App Store Application data (except the Application itself, its tmp, and Caches folder)
- Application settings, preferences, and data, including documents
- In-app purchases
- Game Center account
- Wallpapers
- Location service preferences for apps and websites you've allowed to use your location
- Home screen arrangement
- Installed profiles
When you restore a backup to a different device, installed configuration profiles aren't restored (such as accounts, restrictions, or anything that can be specified through an installed profile). Any accounts or settings that aren't associated with an installed profile will be restored.
- Map bookmarks, recent searches, and the current location displayed in Maps
- Nike + iPod saved workouts and settings
- Paired Bluetooth devices (which you can only use if restored to the same phone that did the backup)
- Saved suggestion corrections
- Trusted hosts that have certificates that can't be verified
- Web clips
The answer remains the same regardless if you are unable to transfer just the photos and videos in the old iPhone's Camera Roll to the new iPhone.
Photos/videos in the iPhone's Camera Roll can be imported by your computer as with any other digital camera.
Import the photos/videos in the iPhone's Camera Roll.
http://support.apple.com/kb/ht4083
The iPhone's backup is stored in a SQLite database format which means you can't simply access the backup to extract photos and other data without using a utility that is designed for it. There is no need to do that unless you have erased the old iPhone.