To get back to the original question (which I'd certainly lost sight of), changing up at 6000 rpm from 3rd to 4th will drop you to 4700 rpm. Now we need a dyno curve, which I don't have to hand. My guess would be that power would be about equal, going from the falling side of the curve in 3rd to the rising side in 4th.
The thread title is
when to change gear: but the original poster didn't say if this was for daily driving or drag-race performance. The two cases will give different answers, not least because in daily driving you have to balance absolute acceleration against the noise, aggravation and general wear and tear on hardware and the driver

My answers are more to do with daily driving, not absolute performance, partly at least because I don't have dyno curves to work with. The differences in performance that win races are not generally significant in daily driving.
So I still say that, for daily driving, there is no point in going over peak power rpm and you want to stay above peak torque.
Pat, my choice of 4K rpm as a change-up target is not from precise measurement, it is just that at 4k the torque is starting to drop off noticably.
Now, torque and power. The two have a fixed relationship, so you can't talk about them in isolation.
Power(bhp)=Torque(lb-ft) x rpm/5252
So the shape of the torque curve affects the power curve: as rpm rises torque starts to drop off above maybe 2000 rpm. so the power only continues to rise as long as the torque curve doesn't drop too fast.
In basic terms: torque is about how big a bang you can make in the combustion chamber, power is about how soon you can make the next one, how many you can make in a second. In a petrol car, higher rpm is always better, right up to the point where the engine falls to bits, although there are lots of things that have to be just right to keep performance rising at higher revs.
In terms of acceleration, flat-out maximum performance will be got by revving past the power peak so that the change up comes where power at the lower revs (rising) is similar to the power at the higher revs (falling) This is why racers spend all their time at high rpm. That's also what the acceleration curves produced above have shown, and there's no arguing with real-world results.
For daily driving, the gains are minimal, and the consequences need to be kept in mind - principally poor mpg. It simply isn't practical to drive all the time as if you were on a racetrack.
So, then, a generalisation to finish with: in daily driving, provided you aren't interested in the last few percent of acceleration, change up at or before the power peak but make sure that you are above the torque peak after the change. This will give a fairly wide range of change options - often referred to as "drivability" - which means you can adapt your driving to road conditions. It can be easy to fixate on performance targets (acceleration, top speed or mpg, say) which is fine until life throws an oil slick, or a wandering child, in your way.