RAM Impact on database operations
The information you provided is not sufficient to analyze the problem, so people will start guessing (BTW how have you established your theory that the problem is memory pressure?). To analyze the problem you need to enable sql_trace for both sessions, even better set event 10046 for both sessions and then compare the data.

this can be done by executing the following sql once the session has been established

alter session set events '10046 trace name context forever, level 12';


This will generate trace files. These trace files need to be analyzed either manually or with tkprof. You need to pay attention to the wait events.

Are there any other differences between the machines in terms of


Processor
Disk speeds and disk types
Network infrastructure
Other load on the machine
Number of database sessions


As these will affect the performance measurements