Hiya
Sorry but I dont know/care why its more efficient! But I would imagine higher turbine operating temp, better fuel burn and airflow through the combustion chambers and overall better airflow through the compressors and turbines has something to do with it.
As for which is better, it depends upon your point of view and experience.
Personally I love the RB211/Trent 'cause it has easy access to most of the major parts under the fan cowls, fan blades are easy to change and general fault finding/trouble shooting is straight forward. I hate the older JT9-D,7Q 'cause its dirty, reversers are a bugger and the cowls are a nightmare to close. JT9-7R4E is a bit better 'cause of the new cowling. CF6-80C2 rarely go wrong reversers are easy to lock out, good oil consumption....I could go on....
As I said before it is all personal experience. But I hope this helps.
Love
Le Pen
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Nil Fault Found.....My A**e