Your i-device was not designed for unique storage of your media. It is not a backup device and media transfer is designed with you maintaining a master copy of your media on a computer which is itself properly backed up against loss. Syncing is one way, computer to device, updating the device content to the content on the computer, not updating or restoring content on a computer. The exception is purchased content.
iTunes Store: Transferring purchases from your iOS device or iPod to a computer - http://support.apple.com/kb/HT1848 - only media purchased from iTunes Store
For transferring other items from an i-device to a computer you will have to use third party commercial software. Examples (check the web for others; this is not an exhaustive listing, nor do I have any idea if they are any good):
- Senuti - http://www.fadingred.com/senuti/
- Phoneview - http://www.ecamm.com/mac/phoneview/
- MusicRescue - http://www.kennettnet.co.uk/products/musicrescue/ - Mac & Windows
- Sharepod (free) - http://download.cnet.com/SharePod/3000-2141_4-10794489.html?tag=mncol;2 - Windows
- Snowfox/iMedia - http://www.mac-videoconverter.com/imedia-transfer-mac.html - Mac & PC
- iexplorer (free) - http://www.macroplant.com/iexplorer/ - Mac&PC
- Yamipod (free) - http://www.yamipod.com/main/modules/downloads/ - PC, Linux, Mac [Still updated for use on newer devices? No edits to site since 2010.]
- 2010 Post by Zevoneer: iPod media recovery options - https://discussions.apple.com/message/11624224 - this is an older post and many of the links are also for old posts, so bear this in mind when reading them.
Syncing to a "New" Computer or replacing a "crashed" Hard Drive - https://discussions.apple.com/docs/DOC-3141 - dates from 2008 and some outdated information now.
Copying Content from your iPod to your Computer - The Definitive Guide - http://www.ilounge.com/index.php/articles/comments/copying-music-from-ipod-to-co mputer/ - Information about use in disk mode pertains only to older model iPods.
Get Your Music Off of Your iPod - http://howto.wired.com/wiki/Get_Your_Music_Off_of_Your_iPod - I am not sure but this may only work with some models and not newer Touch, iPhone, or iPad.
Additional information here https://discussions.apple.com/message/18324797
Assuming that you are running the same iOS on both devices ..... Do you use iTunes? Transfer purchases from the iPod into iTunes, backup the iPod, and sync the phone again. Connect the iPod to iTunes, restore from the backup of the phone and then sync with iTunes.
iPod only apps will appear in their native size on the iPod screen but they will work.
Restoring from the backup will place all of the app data, device settings and documents onto the iPod but you still have to sync with iTunes in order to place of the apps and your other media onto the device.
if you use iCloud only, restore the iPod from the backup of the phone and that will take care of everything.
Some useful and informative information here.
How to backup and restore from a backup