From Airbus FCOM:
The managed climb speed, computed by the FMGS, provides the most economical climb profile as it takes into account weight, actual and predicted winds, ISA deviation and Cost Index (CI). The managed climb speed also takes into account any speed constraints, e.g. the default speed limit which is 250 kt up to 10 000 ft.
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A long time Airbus FBW TRE told us it was better to climb in managed if you can, and I think it was viewed as good practice. I always use managed climb/descent unless there is a good reason not to, (and just in case there is a constraint that I’ve forgotten).
The only statement I can find for Open Climb:
The OPEN CLB mode is a selected mode. It uses the AP/FD pitch mode to maintain a SPD/MACH (selected or managed) while the autothrust (if active) maintains maximum climb thrust.
Nothing about economy, but that’s not to say it doesn’t.