Given that the lower the by-pass ratio, the higher the efficient cruise altitude I would guess the a higher by-pass ratio engine would lower the best economy altitude.
I agree.
High BPR- better for low alt performance
Low BPR- better for high alt performace
A compromise BPR is achieved based on specific aircraft role. e.g. in a two engined commercial jet you need-
a) Good high level cruise ability.
b) Good engine out climb gradient.
So....like everything else in this world.... compromise.
