We loaded some apps on the phone three times each, manually closing them between runs and timing them with a stopwatch. We averaged the three times to get our final result. On this count, iOS 8.1.1 changes little for users with Apple A5-based devices. App load times are basically the same as they've been since the iOS 8 update, and they're still longer than they were under iOS 7.1—Safari is the only one that shows any sign of change that can't be explained by the margin of error, and it's still not a big one.
Noting the limitations of 512MB of RAM on the iPhone 4S and iPad 2, Ars also tested how fast Safari could reload tabs after they'd been purged from memory. In this test there were some minor improvements. Reload time was slighter faster and the site says it didn't run into crashes or instability.
The best we can say is that something about the process of loading and ejecting processes to and from the A5's 512MB of RAM could cause slowness and instability in iOS 8.1, and whatever the problem was has been at least partially addressed in iOS 8.1.1. The update doesn't help with the still-unimpressive performance of the UI, application launches, and lighter multitasking loads, but it does deliver some consistent and measurable improvements under certain circumstances.
After going through all their tests, Ars concluded that iOS 8.1.1 didn't hurt anything, helped sometimes, but isn't an 'iOS-7.1-on-the-iPhone-4-style shot in the arm'.
Let us know your experience with iOS 8.1.1 in the comments. Did it make an improvement?