OK, so there is a backup tool on the PS3 for you to do this. The downside is that since you've already used the new HDD, I don't know if it will overwrite what's on there.
To use this tool you need:
1) Old hard drive (installed in PS3)
2) A USB memory stick (I used a 16GB one)
3) New Hard Drive
Now, you're limited to what you can do in regards to the space you have on said memory stick. For me, I just wanted to move my save data - I was OK with having to download DLC/games again or having install times. That's really the only caveat here. You could also theoretically use a third hard drive for this, should you have one sitting around.
So, here are the steps to take.
1) With the old hard drive in the system, delete all data that is NOT needed to transfer (Movies, music, install data, etc.)
2) When you have your HD down to a size that will fit on the memory stick/backup hard drive, plug that baby in, and go System Settings -> Backup Utility
3) Select the backup option. Follow all of the steps and back up onto your memory stick.
4) Turn off the PS3, and install your new hard drive.
5) Go to system settings -> Backup Utility, and this time select restore.
6) All of your data will be transfered to the new hard drive.
Like I said, I don't have experience with this in regards to having used the new HDD already, but that's the standard, Sony way of backing up PS3 data.