I am really interested in story writing for video game development but I am not sure if a degree in Game Development or English would be more desired over the other. What are some recommendations?

Common wisdom is that there is exactly one job for which an English degree is useful: English professor. That's probably not quite true, but it's also not too far removed from the truth. Most successful authors don't have English degrees, and most of those who do don't credit their degree with teaching them anything useful.

The important question isn't what looks better on your resume but which path is going to teach you the skills you need. And the answer is probably neither one. An English degree isn't going to teach you how to write. A game development degree also isn't going to teach you how to write. Writing (and getting feedback on what you've written, and actually using that feedback to improve your skills) is going to teach you how to write.