I have a Cisco AP 1602 and have two SSIDs, one for the corporate network and the second one for the guest network.
Users claim that the guest wifi is slow, but while connecting to the corporate one, internet is fine.
That is a dual band access point. Any chance one is connecting to the 5Ghz radio and the other to the 2.4Ghz radio.
Check out a sample case and see if this might be the case.