The process reasoning is covered well by 25362. However, other reasons are based on eceonomics: eg. a very tall vessel is less ecomomical to build than a horizontal vessel; because of the civil fdn etc and wind loads.
On the otherhand if a smaller vessel is installed horizontally, it requires a larger foot print.
Typically, both horizontal and vertical vessels will do the job; so compare the tonnage for both options and go for the cheaper one. Of course you do not want your separator to look like a tall pipe.