Puritan Board Junior
The biggest differences would be that possession implies ownership and in a universe where Jesus Christ is Lord, the Creator and all things are his I don't like the idea that satan owns anything.
Secondly, possession really isn't a biblical word. Daimonizomai, on the other hand, appears 13 times in the New Testament.
In the parable of the strong man bound Jesus did refer to the prize as "his" goods. It seems that de facto Satan still "owns" some people.
While there are Scriptures that refer to Satan's present loss of power, does that loss, as a practical matter, affect anyone other than the elect?