There is really little difference between se and ee versions of the database.
How many physical CPUs does your server have?
If more than 4 then you have to go ee only as se is licensed up to a max of 4 CPUs.
This is the starting point in any discussion. The next thing to consider is cost, se is about 11k per CPU whereas ee is approx 33k per cpu core, then you have to pay for the first years support which is approx 22% per license.
Now down to the actual database itself.
Some of the fundamental differences between se and ee
With se you cannot do online index rebuilds, you can only use a single channel for Rman backups, you cannot set mttr parameter or flashback (I think)
You can like ee use stats pack for performance tuning.
For More Information Please See this document:https://prakashoracledba.files.wordpress.com/2015/03/oracle-database-comparisions-of-various-editions.pdf
Hope this helps