Hydrolysis of polyesters Watch
The rate-determining step is clearly formation of one of the initial tetrahedral intermediates. In alkaline solution, OH- attacks a carbonyl. In acid, H2O attacks a protonated carbonyl.
Without looking anything up, I'd say this means OH- is more activated compared to H2O than is the protonated carbonyl compared to the carbonyl. I guess you could put this in MO theory terms to if you wanted to be more quantitative.