Max PSID wouldn't really affect this situation as the respective aircraft are not operating at their maximum altitudes.

I don't have any information as to what AA SOP for cabin pressure altitude on the MD-80 vs. the 737. The 737NG does have a higher max PSID, but that doesn't mean that it operates at a lower cabin altitude.

As fanger said, it's more to do with the rate of change rather than maximums for level of comfort. It could be that SOP for AA MD-80s calls for a lower vertical speed of cabin pressure than 737s, but you'd have to find out from an AA pilot.