If a picture paints a thousand words I guess a video paints a million.
Unfortunately, while I don't doubt that there are people facing problems, they provide so little diagnostic data that it is hard to help them. There are so many ways in which the phone's performance could be compromised, and so many individual ways to tweak and tailor the phone to improve things, but a brief few words to say "It's laggy after the upgrade." are hardly the basis for understanding what is wrong and what can be done to improve matters.
I wouldn't say that my own experience was without problems, but my grumbles were down to battery life rather than operational speed. Now I seem to have overcome that hurdle, but my approach was to go back to absolute basics - full factory reset and install no further apps apart from stock. I also disabled the bloatware I have no interest in and will never use - stuff that is well known to waste data and suck power such as Flipboard, Google+ and a myriad other bloaty apps. I also binned all the stock home screens and set a single, widget free home screen with black, static wallpaper. I've tried Google Now, but I'm unimpressed so far and have disabled that. Basically the phone is only running what I want it to and not the things Samsung (or Google) thinks I might like.
After a couple of days without drama I started adding back a few of my own apps, like CoPilot, but really cutting back on the apps I seldom/never use. So far so good.
It's anybody's guess what might be wrong with the more troublesome machines out there, because none of us but the owner has a clue what they've actually done with the phone. And let's face it, some of these devices could be well and truly clogged up with a mire of dreadful apps which hog resources and cause problems which have nothing to do with Samsung or the JB upgrade. Conceivably the JB upgrade may have made things worse, or perhaps it simply did not turn out to be the silver bullet that people were expecting. As upgrades go there doesn't seem to be a lot to tempt me. The most interesting thing for me is the
customisable notification bar toggle widget, which I'm sure ICS did not have. Apart from that I am ambivalent about any other "improvements" brought by JB.