No, External hard drives work the same as an internal HDDs. You can use the same programs for file recovery. Also, the drive format does matter but I think you'll find that the majority of recovery programs will recover files from both NTFS and FAT32. But you'll have to read what the software is capable of to know for sure.
I used this FREE program to recover thousands of files from a drive that failed on me.
I use Acronis True Image to make an EXACT snapshot of my Windows C-Drive. I have one I made after all programs and tweaks were made and I have a second one that gets AUTOMATICALLY updated (can update daily if need be). After a few months, I delete that second Automatic one and start again.
If you have Windows XP or higher you should be using NTFS. If you have FAT32 you should convert; it`s very simple and you can easily Google the instructions (FAT32 to NTFS convert).
You should store the backup Image(s) on a second hard drive, either internally or USB.
Example of how to use:
1) Help! the main hard drive is dead or I have major software corruption.
2) Replace the main drive if broken.
3) Export or copy any files like e-mail etc if you have NOT backed those up recently.
4) Insert the Acronis Boot CD or start from within Windows
5) Choose RESTORE and find the backup Image that you want (usually the recent, Automatically updating version on your second hard drive)
This program is invaluable. Windows does have a System Restore feature but it`s not perfect. Acronis TI makes an exact image that you can use to get back to the EXACT state of Windows (including all your data). That`s also the drawback. You need to make sure you have backed up your files but again, the Automatic backup version is the best way to go, simply choose the last date before your system got screwed up.
*The best setup is:
1) a faster hard drive for Windows (like a WD 640GB Black)
2) a slower, quieter hard drive for backup and storage (like a WD 1TB Green)
3) Optionally a networked drive or USB drive just in case your entire computer is stolen