IME, if it is a 'long term' change, you will get to know several weeks in advance - I got to know we were flying the A380 insted of 777 when Airbus preponed the delivery of its A380 and EK deployed it on DXB-JFK in August instead of Sep 2008. Also when EK kept postponing upguaging EK029/030 to A380 from a 777.

However, it is an 'opportunistic' or 'operational' change (substituting a 77L in place of 77W or one of the older aircraft with skycruisers instead of suites), you will only get to know about it when the flight leaves DXB.