Windows 7: Can I have an external hard drive work on both vista and 7?

So My new computer build is having trouble using a certain program I like to download stuff with but my laptop can use the program no problem. My external was always hooked up to my laptop which is running vista but when I try and view the files on my desktop (running 7) it cannot look into the hard drive and see the files. I was curious if I just bit the bullet and formatted the hard drive on windows seven would it still be compatible with my vista laptop so I could download files on my laptop and move them over to my desktop with the external? Or is there a way I can have the hard drive work for both without deleting all the files?

The external should work in both the computers.

If you plug it in to the desktop, nothing shows up there in the explorer ?

Does it show up in the disk management window ?

nothing shows up in explorer but when I go to administrative tools and then disk management it shows up. I go to assign it a drive path and it keeps coming up with an error saying the window needs to be refreshed so I refresh it, nothing changes, restart my computer, nothing changes. The only other option is to reformat it but I don't want to do that unless I absolutely have to because all my files will be erased right?

Can you back the date up in laptop, and format it ?

When done, you may put those data back to the external again.

Yea I will lose some files because my laptop hard dive is smaller than my external but its looking like that is the only option

A few DVDs may contain the other data

i have like 230 gb of movies that I don't have space for.... lol I don't think I'll be able to save those