Why do electrolytics have a different charge and discharge rate for the same current
Two suggestions:


  The curves are really flat (the charge has a very slight curve).


The charge has a curve because your caps are unbalanced. One of them has lower capacitance, it charges faster than the others, then it hits breakdown voltage and begins to leak. When discharging the issue does not exist. Thus charge is curved, but discharge is not.

How to distinguish this from soakage/dielectric absorption: charge, then wait monitoring current, if dielectric absorption is not involved then current will be negligible.

Suggestion 2 is I'm wrong ;) in this case I'm interested in the real answer!