As an illustration of the different effectiveness of Watts depending on speed I worked through the following scenario on a power/speed calculator, with weight (75Kg), wind, drag, frontal area, etc., all remaining fixed at sensible values.
Imagine a course with 6 miles flat at 0% and then 1.85 miles rising at 10%, and imagine you can average 250 Watts for around half an hour, a realistic power around FTP for a 75kg Active Fitness Level cyclist,
Taken at a steady 250W, this would take 33.7 minutes, obviously at an average power of 250W
Now imagine if you spend a few more watts on the flat bits, say 20% more to go at 300W for 15 minutes,
Since this is above your FTP, this means you will have less energy when you reach the climb and your power drops to around 214W, giving the same 250W average
The whole course actually takes nearly 2 minutes longer even though the average watts is the same.
Since we know you can maintain 300 Watts for 15 minutes lets imagine instead you save your effort for the climb, and climb the 1.85 miles at 300W, which takes the same 15 minutes
To maintain the same average power you need to conserve a little energy on the flat so you ride at 206.5 Watts to give the same 250W average.
Although you have averaged the same 250 Watts, and managed 300 Watts for the same 15 minutes, you take 3 1/2 minutes less in total, a 10% saving and quite a handsome lead in a race.
In fact, although you averaged the same 250 Watts, you had to maintain this power for 10% less time, and therefore should be less tired, even though you were considerably faster, and would probably have more left for a last minute sprint!
I would say that if you ride to average around your FTP, but use any AWC (Additional Work Capacity) on the steeper gradients, and recharge on the flats and especially downhill, you will average a faster pace and ride for a shorter time than if you put your efforts in on the flatter bits!
Geoff