In general, everyone that gives advice on this says to never enable auto-close because it just causes unnecessary delay when a user queries the database after it's been closed, along with a spike in resource utilization when a database has to come online. And in general, that is golden advice for databases that are used on a daily basis.
However, when you get outside the theoretical perfect environment where every production database is really in production, it may make sense to enable auto-close in some instances if the following conditions are met:
There is a large number of databases that contain only archive data that is queried infrequently (less than once per day, for example).
The users are aware that there will be some delay the first time they query the database after it's been idle for a while, and they are OK with that.
Due to data retention policies requiring the data to stay around long after it's no longer used on a daily basis, and the struggle to get business units to actually decommission database they aren't using, it is certainly reasonable that auto-close might make sense in some cases. If it can lower your hardware resource requirements and still meet the users' needs, it may be something to seriously, but cautiously, consider.
As for the memory allocation difference cited, there is no way to be sure what caused the difference without more information.