For the B777-200ER fitted with the GE - Pratt - RR; here is the ICAO fuel burn data.
GE-94B - Take-off - 3.513 kg/s
Pratt 4090-Take-off - 3.926 kg/s
RR 895 - Take-off - 4.03 kg/s
GE-94B - Climb-out - 2.831 kg/s
Pratt 4090- Climb-out - 2.996 kg/s
RR 895 - Climb-out - 3.19 kg/s.
So from the above data, the RR burns the most fuel during take-off and also in the climb-out.
I have yet to see good data to prove otherwise.