Looking on the internet deeply has found these results:

mission complete is the most popular phrase on the web.

mission successful 1113,000 results on the web	mission complete 1363,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
I don't like the idea of gunplay, but the mission was successful. Today was our 30th successful mission. As regards peace You'd be temporarily reinstated in the Forces, and if the mission's successful, there may be a presidential pardon. The mission was successful but later a very tragic sacrifice followed. Indeed. We hope her mission is successful. Six days. I understand the mission was successful, sir. My trade mission was Successful, Thank you for asking.	I will not leave until our mission is complete. Tony, I believe the mission is complete. We have the Intersect Cube, Fulcrum is defeated, your mission complete. I am to stay until this mission is complete. We have Dr. Whitehall's mission to complete. I want ares back online and his mission complete. I still have a mission to complete. Yes, mission complete, Arsenal.

mission successful

1113,000 results on the web

mission complete

1363,000 results on the web

More popular!

I don't like the idea of gunplay, but the mission was successful.
Today was our 30th successful mission.
As regards peace
You'd be temporarily reinstated in the Forces, and if the mission's successful, there may be a presidential pardon.
The mission was successful but later a very tragic sacrifice followed.
Indeed. We hope her mission is successful.
Six days. I understand the mission was successful, sir.
My trade mission was Successful, Thank you for asking.