Don't think that only the Rolls large fan engines are triple-shaft .....
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I was then asked if I knew why Rolls decided to go with the triple spool design and PW didn't.
Doubtless because the Rolls was designed later. Both current Pratt and GE engines are nothing more than refined and extended versions of the engines first designed in the early 1960s for the C-5 Galaxy. Rolls were a few years after this putting the RB211 design together, in which time technology had advanced notably.
There can't be a fundamental difference because Pratts and GE never redesigned for triples, and Rolls never redesigned to go back to twins.
In the days of steamships 100 years ago there were compound steam engines which had either two, or three, or four stages of expansion of the steam. None triumphed over the other, but then the steam turbine, and then the diesel, came along and swept it all away.