On my iPad Mini, 7 doesn't seem perceptibly any faster or slower than 6.1.x -- just different, which is a topic for another thread.
My iPhone 4S, however, is a different story. It does indeed feel noticeably choppier/more sluggish in some respects. The dropping-out-of-warp starfield simulation the icons do when unlocking, for instance, often seems quite herky-jerky. There are other, intermittent, occurrences where the OS seems to just pause for a moment or two while it performs some sort of background process (clearing/swapping RAM contenets, perhaps), that just makes the whole experience of using the phone a tad more Jedi/Zen-like -- "patience, my young padawan". My 4S has only 16GB of storage, but 3GB free, so swapping RAM contents *shouldn't* be a problem of available space, no?
And now if you'll permit me to mix metaphors -- that's my two cents, your mileage may vary.