Several people's responses basically said that they wouldn't improve the experience at all.
For some people, it wouldn't.
My husband is a perfect case in point: I can show him any cool tweak on my jailbroken iPhone. He smiles, nods, and says he doesn't need it--and then it's suddenly cool and amazing two years later when Apple incorporates a less useful version of it into their firmware.

Hell, he doesn't use half the functionality on the stock iOS. He also likes being able to update whenever Apple tells him to. (He does this on the iMac too...which is why I have a separate computer.) In his mind, iOS "just works" as is, even when it doesn't, and he doesn't really notice the things that drive me nuts about it. I stopped trying to reason with him about it years ago.
He'd also never be able to triage his own phone if something went sideways. And my personal rule on jailbreaking is that I won't act as technical support if something goes wrong for any friends or family who want to try it. I have to do more than enough of that with stock devices!
That said, I'm deeply amused at all the people who say a jailbroken phone is inherently unstable. I've jailbroken on four iOS versions so far, and had no major issues in spite of having a pretty heavily tweaked phone. Contrast that to darling hubby...who has been swearing at his fully updated iOS 8.xx iPhone 5 & iPad Air an awful lot lately.
Having a stable, jailbroken iPhone is all a matter of what you put on it. Well known devs within the JB community work hard to ensure their tweaks are as reliable as anything you'd get from the App Store (and more reliable than Apple, lately!) If you don't pirate apps and wait for others to try the newest tweaks first, you probably won't run into any major conflicts and your phone will continue to run smoothly...but with better functionality than Apple designed for it.