hi.
Why you not try to just compare access plan of SQL statements on QA and Prod.
If refresh of data on QA not so old and the plans is different then you must find a reason why it happen (broken indexes, statistics or data size increased so optimizer uses another access plan).
If your system migrated to another vendor then it can use different HW and disks. And I think it possible that data distribution on disks was changed (tablespaces and etc). And also some DB settings need to be adjusted. I agree with Sander that you need to involve DBA to make performance trace.
For example, few days ago we moved our saptempdb to another disk (it was already mounted to BW but was not used) and BW performance become very bad. After moving of the saptempdb back we got performance back...