iOS 7 and 7.1 were about the same in terms of UI smoothness, perhaps 7.1 was a bit better but nothing major from what I remember. Anyway, 7.0.x was HORRIBLE with stability and the UI animations were just really slow. Also, the pinch to close gesture for apps was extremely weird looking, the apps would come in as you were still pinching to close, but they did so in a very stuttery way. Also, the dock would look glitchy as that was sliding up. iOS 7.0.x also had tons of springboard crashes, I probably saw the thing crash to the Apple logo several times a week. (Was an issue with all 64 bit devices at the time)
Anyway, the glorified iOS 7.1.2 was still far from finished. It had the same stutter with anything involving the keyboard, turning slide to power off, turning the App Store, turning spotlight search, Siri animation was still iffy, control center and Notification Center still were a mess on the lock screen and over open folders. iOS 8 pretty much intensified all of these, with a couple new ones. The animation for sending a message is a bit stuttery if the conversation is already filling the whole screen or more, and if I'm sending a longer message, it was much smoother in that regard in iOS 7, if I remember correctly. Oh, and after I have been using an app for awhile (or the app is intensive) the "App to home screen" animation is really stuttery, or it skips almost the entire animation so you just see the last split second of it. Pretty weird. Haven't had anyone else report this, but I have done a full DFU restore and it's still there. It isn't as bad as it was, but it... Definitely is still there. I believe iOS 7 would just hesitate, and then leave the app perfectly smoothly.