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?

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?

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

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