I say update.
The main difference between 5.0.1 and 5.1.1 on an iPhone 4 is stability and battery life.
The battery life fixes apply to all devices that can be on 5.1.1. Not just the 4S (even tho that's what Apple said).
My battery life has increase a noticeably good amount since updating to 5.1.1.
Second:
The jailbreak is much more stable then 5.0.1. In fact I think 5.1.1 is more stable then 5.0.1 period.
If I were you I would restore to 5.1.1, setup as new device, not from backup (as that greatly enhances the stability of any jailbreak ALOT).
After restore...and you went through the initial setup of the phone (rite when you first get access to the SpringBoard) don't do anything at that point. Don't configure anything.
Now jailbreak with Absinthe. Make sure it's the latest version 2.0.4. (do not use the "Erase All Content and Settings" option before jailbreaking)
After jailbreak, don't open Cydia.
Sync your music, apps, ringtones,etc from iTunes.
After your done with iTunes...open Cydia and enjoy.
I believe these steps "exactly" will yield the most stable jailbreak.
As that is what I do every time a new jailbreak comes out for a new iOS.
I restore then jailbreak...and I restore again..then jailbreak again, and I restore again...until I figured out the exact steps to make the jailbreak "100%" stable and flawless.
If I see one tiny little minor thing out if place...I restore and jailbreak again...of coarse doing things a little differently each time.