I'm fairly sure that F-16 is more agile than F-15.
Not exactly, the F-15 and the F-16 are not designed to be a vs. comparison. These two compliment each other and form the USAF's Hi-Lo (or Hi-Mid) tier. The F-22's designed was based on F-15's characteristics.
F-15 is designed only for air dominance (with the exception of F-15E), it is supposed to fly high, use its bigger radar and other EM suites and kill the enemy from long distances (its replacement is F-22 so they both do the same thing in their times). At the time the F-15 was being introduced, the USAF had F-4, F-111, F-14 and F-15's. As you can see, these are ALL heavy duty jets. Good to form the top tier but hard to deal with more agile jets like Mig-21, 23, 29, Mirage F1, etc.
Then the F-16 was primarily designed to counter the small Russian armada using Migs and other proliferated copies of Mirage, etc. The primary goal was agility and multirole as Migs were small and very agile.
So from a core designs perspective, these two jets compliment each other and shouldn't really be compared. However, the US didn't want to whole sale F-15 as it formed the High tier of the USAF. The F-16 became an international history and thus, the need came to constantly advancing this plane as it was facing Mirage 2000, Mig 29, etc with more advance avionics. As a result, you saw constant advancements to the F-16 as it became a cash making cow vs. the F-15. Which was already above the capability standards.
Post 2000, if you compare both, the evolution in semi conductor industry's made advanced avionics with smaller sizes so both the planes have somewhat the same capabilities. The exceptions are, F-16's true mufti-role capability, its agility, current avionics and an excellent man-machine interface.
While the F-15 saw less of the 'so many upgrades' to the F-15's. But these jets were upgraded to house state of the art avionics. It has long detection and radar range and bigger bvr payload (unless you want the F-16 to carry bvrs on all stations to compete the weapon carrying capability in an AA engagement. F-15's do enjoy longer detect-track range, longer endurance, higher speed due to twin turbines and advanced electronics suite