Both are common and acceptable in casual speech.
-1- "It is a really unforgettable experience" is weak because unforgettable is an ungradable adjective.
- The meal was good. (correct)
- The meal was very good. (correct)
- The meal was really good. (correct - here really good is a synonym for very good)
- The meal was unforgettable. (correct)
- The meal was very unforgettable. (weak - very unforgettable doesn't work)
- The meal was really unforgettable. (weak - really unforgettable doesn't work)
-2- "It is really an unforgettable experience." This is an emphatic statement, often used to contradict an earlier statement.
- I heard Paris is not as wonderful as it seems in the movies.
- No, no, no! Paris is really an unforgettable experience! We enjoyed the Louvre, the Eiffel tower, and the wonderful food!