CTEvsSTA
Each tool works on the algorithms.. the better the algorithm the better the tool.. Encounter / First Encounter is a general P&R tool which concentrates mainly on placement,CTS and Routing.. CTE is a dedicated timing tool. though FE has timing tool within itself, the algorithm for the timing here in encounter is not so exhaustive.. so you will find differences...
This is the reason why most of the customers ask to signoff the chip using std timing tools like Prime Time.