The only thing they have in common is they both operate fuel flow limits and use energy recovery after that the concepts are different.
LMP1 power units have pretty open regulations as in there are many possible engine configurations that can be used. I don't think there are any limits on engine size or layout.
In F1 you must use a 1.6 litre V6 where a lot of the mayor dimensions are fixed as in bore stroke angle of the 'V' length etc and the turbo must be on a certain axis to name but a few.
It would be possible to run an F1 engine in LMP1, but how good it would be I don't know.
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