My experience is that with a decent bit of round bar - IE pretty good circularity - the four jaw holds it more firmly. It feels a bit more rigid when turning. If the circularity is a bit irregular it may not be so firm, and of course the three jaw will hold any bar. Obviously the four jaw is good for square bar, and octagonal if you can find some! I saw a three jaw independent the other day, and I can't see what that would be good for. It would be a right pain to adjust.
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But from the original post I can't see how a four jaw self centring chuck helps with reducing a bit of 25 mm square bar down to 24 mm square. I see that as a milling job - or get a decent file out. It can be done as an extreme (in Unimat terms) job for the four jaw independent chuck. I could even do it in the three jaw self centring, now that I think about it, but it would not be pretty.
