A lot of things a slightly different when you run your application on cloud services like AWS. Take database servers: Increased load can always change the performance of DB look-ups and writes. Larger tables can lead to slow queries if the tables are not indexed right, a lot of writes may cause unexpected locking, etc.
However if you use Amazon's AWS there is another important factor you should not loose sight of: IOPS. This measures the number of I/O operations between the database server and its storage, which is attached as network storage.
It's somewhat unclear if/how Amazon throttles the throughput if you don't reserve IOPS. You might be at the mercy of other RDS instances that are running on the machine and probably some kind of rate limit AWS implicitly imposes.