Performance
I guess the main reason why people go for it is the performance. So how does it compare? On the road, there is a marked difference in acceleration and power. Like another owner described, on a B road the ability to make a quick overtake is almost bike like and you can make safe overtakes in places you just couldn't before.
The sense of thrust is a fun sensation and call me a kid but seeing cars shrink in the rear view mirror can be fun from time to time. It taps into a primal sense; the thrill of acceleration.
I would say it is no faster A to B on the road, in fact the way the power is delivered means you need to be more careful whereas a standard tubby you can probably be earlier on the throttle and more confident.
I think a stage 2 is more satisfying on the road. Stage 2 has a lovely balance of power that you can exploit and for that reason it's more fun to wring the neck out. By contrast the stage 4 has too much power to wring its neck out so you have to be much more measured on how you apply the throttle.
On a recent back road drive in Europe this became more apparent. The car was great for zipping past people which helped country road progress but ultimately not as much fun through the twisties. Half way through I realised there was something missing in terms of the full satisfaction I was getting compared to that same drive a year ago and I found myself feeling not quite as satisfied as before. For me it's a subtle difference as the drive was still fun but it was noticeable. You simply can't exploit it's full power on the twisties without being dangerous. As a result the drive was not as satisfying.
So it has it's pluses and minuses.
What about on the track?
It depends on what track it is, if it's a twistie one then there won't be much difference. Faster tracks and there will be. It's nice to be able to have the power to dispatch those annoying cars that have high bhp, rubbish round bends and poor drivers who have an ego problem about letting people past.
Here is an on track comparison. At Brands the stage 4 car was just quicker by a second, both times were on the same Khumos.
The Spa comparison is not strictly fair as the Stage 4 was also on 888s but you still get the idea of the difference. It's the steepness of the rising traces to look at. The downslopes should be very similar whatever state of tune. You can see the steeper acceleration trace leading to much higher top speeds much more quickly.

You can see the time difference that extra power makes in terms of time gained. (part of that gain is due to more familiarity of the track). If you took out that factor and the different tyres then it is probably somewhere around 5 seconds quicker as a result of the extra power.
Does a stage 4 make track work any more fun than a stage 2? For me, not really, I'd say the same amount of immense fun with stage 4 having the added advantage of not getting snagged up with fast 'straight line' cars. You can also let rip with the power in a way you never can on the road, so it's satisfying. So it just wins in terms of track use, but with the danger that it makes you a lazy track driver as it hides errors of not carrying enough corner speed, that in a slower car would be obvious by the time you got on the straights.
Overall my advice is don't rush into stage 4, it's not the holy grail. Really learn and enjoy your car, you might find that it's current state of tune is just right. If you are going to go down the modification path resist stage 4 as the starting point. Go to stage 2, do the suspension, uprate the pads, the discs. And really wring it's neck out whilst having a manic grin on your face.