Look at the TDF riders
The riders in the TDF averaged significantly faster speeds on the level stages as compared with the mountainous ones. On the level ones they were often averaging 27-28 mph. On the mountainous ones they were averaging closer to 20 mph - some were even below 20 mph. Also, on the flats the riders for the most part all stayed together, whereas in the mountains huge time gaps opened up and some riders (memorably Tom Boonen) had to drop out.
To answer the question of which is faster, consider an extreme example. Suppose you were riding a 100 mile course where you first rode 50 miles up a mountain and then 50 miles down. Suppose going up it was so steep you could only average 5 mph. It would take you 10 hours to ride this first half. Even if you could somehow (impossibly) do the descent instantaneously, your century time would still be 10 hours - not too good. In all likelihood you'd be able to do a flat century much faster than the 10 mph average you would have attained on this mountainous course. Basically, just mentally picture a course with a hill so steep and long that you could barely move up it - there is no way that descending that same hill again could possibly regain all of the time lost on the ascent.