Not sure if this is possible but I'm looking to transfer all my 360 content from my 250GB HDD to a 500GB HDD but my issue is I don't have an official transfer cable, I do have a sata to usb cable for PC and I have read I can use a data recovery to read and save the data to my PC, but my issue would be how would I transfer the data from PC to the HDD
You can use FATXplorer to read the data in the drive and copy it to your PC, then you can do the same and copy it back to the new hard drive. Depending on the hard drive you would need to take it out the enclosure, which is explained with photos on the tutorial here: Hack a 250gb, 320gb or 500gb Sata harddrive to work in the Xbox 360 and Xbox 360 Slim.