Regardless of maker, there's no short answer to this ... and it's endlessly debated.
My experience is, from 35+ years in the trade, is that it entirely depends on what crank you have and why it is creaking.
As a generality - JIS does not normally engage far enough into the square taper, plus you are losing the engagement at the "fat" end of the taper which means that proportionately you are losing a lot of the support for the load that you are putting on the crank. The taper angle of the tapers is the same (2 degrees), so it is mostly just a matter of load bearing area.
The nett effect *can* be a tiny amount of movement - hence the creak - and if that movement persists, you will get distortion of the square taper in the crank that can't be rectified by any economic means (machining out a bigger taper and making an axle to suit is scarcely economic).
If you are really unlucky, you can get a crack propogating from the corner of one of the tapers in the crank allowing more movement. This scraps the crank.
Specifically - Older Campag cranks and the current Pista crank, because they use(d) a proprietary taper and may, if older, also have repeat-fitting wear and tear, can fit further up a JIS taper but then a secondary problem can kick in, which is that the taper may not be long enough and the crank comes up against the end of the taper where is "scallops" into the cylindrical shape of the BB axle. In this case, too, a crack can propogate from the corner of the crank taper as this point is over-loaded by the curvature at the end of the taper. This likewise scraps the crank.
Older and the current Pista Campag cranks need to sit on their own proprietary taper to avoid these sorts of problems.
More current (since the end of C-Record) cranks work best on a standard ISO taper.
If you are lucky, you'll have had just a bit of squirm, light damage and re-mounting on a Campag BB should be fine.
Look carefully for any evidence of cracking or distortion in the corners, especially, of the taper in the crank, though. Distortion (burring) is possible but you might get away with it.
Use a Campag BB. They know what their tolerances are and make accordingly. ISO defines the taper angle and starting / finishing square dims. It does not necessarily define the interpretation of those numbers for every manufacturer ... a tolerance is included but some makers will work to a tighter tolerance as a matter of course - if you get (say) a crank maker applying a "tight" interpretation of the tolerance and a BB maker employing a "loose" interpretation and each is at the limit of the tolerance band, it's not impossible that a problem will occur.
Fit the cranks dry and tighten to the required (40-45 nm) torque on the end-bolts.
If you need to exceed the 40-45 nm to prevent noise, or if you are frequently having to re-tighten the end bolts, or both ... you probably have damage that can't be rectified.