The reaction involved is the enzyme catalysed intermolecular reaction of chorismate to prephenate
There is a very nice story behind this reaction. May I ask where you are working, just because I'm interested;)
concerning your question, I am afraid I still can't say anything. I assume you use some kind of Force-Field for the MM, which one do you use? I personally would assume that this approach just fails completely if you're looking at an Enzyme catalysed pericyclic reaction as a claisen rearrangement.
concerning QM: did you use DFT or some HF-related method? which Basis set? how did you model the protein? ...?
from my point of you, I would be very critical about both approaches, so I don't think you get an answer why the QM result is lower... why is this the question anyway? did you compare it with experiments?