What difference is there between them that would make one react differently from contact with a stock's fore end compared to the other?
I don't know for sure, because you can't know. I assume you understand that two "identical" rifles will shoot different loads well. A specific gun will "like" one bullet/powder combination that another will shoot very badly. I don't know why.
I assume you know that two "identical" rifles will get very different velocity numbers from the same load. I don't know why.
I assume you know about things like the Browning Boss system, and about those ugly barrel harmonic things you stick on the barrel and slide up and down to improve accuracy.
I assume you know that there have been bench rest shooters who actually glued their rifle barrels to the stock for the full length of the stock and got exceptional accuracy. (Google it)
I assume you know there are serious differences in barrel harmonics in a 25 pound bench rest rifle and say, a Win Ultralight. Barrel length, thickness, material, fluting, all have an unpredictable effect on accuracy. My experience is that free floating MAY improve accuracy; a pressure point MAY improve accuracy. The only way to tell is to try it.
Every barrel is unique, and the only way to find out what it needs to be accurate is to experiment. But there is no rule that free floating any given barrel will improve its accuracy.