I have an iPad 2 and an iPhone 4S. I upgraded the iPad 2 first and had problems so I decided to leave the iPhone on iOS 7. I certainly don't regret that. My iPhone is working splendidly but the iPad is causing me grief. I agree that there is always going to be a downside to hanging onto a device rather than replacing it every year or so. However, if Apple had put out some kind of statement cautioning owners of older devices to think twice about installing iOS 8, then I would not be so frustrated. Surely they must have tested the new OS on a range of devices and been aware that there would be signifiant performance issues for owners of older devices.
It's the lag that annoys me most. It's intermittent and mostly with Safari. I type something but nothing appears on the screen and then suddenly everything appears in bunch a second or two later. Then it'll be fine for a bit. Even more annoying is the way in which the device becomes unresponsive to touch. Agan this is mostly with Safari. I click on a link and nothing happens, I click again and again ... nothing. Then suddenly it's responsive again and I find myself rick-rolled into random click-bait. That's enough to make anyone grumpy. I also have the problem with Safari crashing and the application just disappearing. But my battery life seems okay.
But, being constructive about this, it's clear from these posts that I've not done enough yet. I installed iOS 8.1.1 though iTunes but I didn't do a complete wipe and reinstall. So I'll give that a shot (following instructions earlier in this list).
Thank you to everyone who contributed in the past few days. It's been very helpful.