Am I likely to get a performance improvement upgrading iphone 4 from ios6 to 7.1? I have an iPhone 4 that I didn't upgrade to iO7 because I'd heard a lot of people saying it hurt the phone's performance, and my phone's performance was already pretty terrible.

I've seen people saying that 7.1 is specifically faster for an iPhone 4, but only in comparison to iOs 7.0

If I upgrade my iphone 4 to 7.1 will it run better or worse? I use it as a backup device, mainly for music, so I'm ok doing without the improvements, but if I'm likely to get a performance improvement than I'm all over it.
7.1 is probably the best performance that you'll see on the iPhone 4. While the loading times for apps seems to be cut by a half a second or more for most, there's only so much you can do for a 4-year-old processor. I'd say the upgrade is well worth it. You won't see all the features that the 4S and 5 iterations see, but its still an increase in performance -- I'd say go for it.