You should transfer your iTunes library from your PC to your Mac so it is still syncing with the same library. Media transfer is designed to be computer to device, not the other way around except purchases from the iTunes Store.
iTunes: How to move [or copy] your music [library] to a new computer [or another drive] - http://support.apple.com/kb/HT4527 - a somewhat bewildering and not always easily understandable set of options.
Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive. Open iTunes and immediately hold down the Option (alt) key (shift on Windows), then guide it to the new location of the iTunes Library.itl file in the moved iTunes folder.
Windows users see tip at: https://discussions.apple.com/message/18879381
iTunes Store: Transferring purchases from your iOS device or iPod to a computer - http://support.apple.com/kb/HT1848 - only purchases from iTunes Store
That is the best way. You can pay for third party software to let you download items but I think they arrive in an unstructured form so if you value the library in its entirety I would transfer it. A NTFS drive can be read by Macs but Macs won't write to it (may not matter in this case). FAT can be both read and write, with limitations that likely don't apply in this situation. If necessary you can copy the folder in parts but make sure they get back together.
iPhone backup files are stored in a different location should you wish to move them too:
http://osxdaily.com/2009/09/11/iphone-backup-location/ - in Mac OS X your iPhone files are backed up at the following location: ~(your home directoy)/Library/Application Support/MobileSync/Backup/
in Windows XP:
C:\Documents and Settings\user\Application Data\Apple Computer\MobileSync\Backup
in Windows Vista, Windows 7:
Anything you have purchased from Apple can be copied off using the instructions I posted earlier. Items from other sources you have to use third party software or move the library.