That's not the story as told about John Boyd and the F-16. By building it light, it ended up with great range and great maneuverability and decent firepower.
The only advantages the F-16 has are cost (a smaller single-engine jet is cheaper to maintain than a larger twin-engine plane), RCS (the typical F-16 will have a smaller radar cross section than a typical F-15, although this is a moot point since the 'smaller' RCS of the F-16 will still stand out BIG on any modern radar operated by the US, its allies, Russia, China, etc), and WVR maneuverability (although, again, this is a moot point since the F-15 can do a lot in WVR, and with the advent of helmet-slaved IIR-missiles WVR is basically a death zone since looks do kill).
Thus, the only real advantage an F-16 has over the F-15 is cost (purchase, maintenance, life costs, you name it). A Viper is cheaper than an Eagle. The F-16 is probably a better multi-role fighter when looked at from a bang-for-buck angle, since the typical F-16 will do a good job in every area A2A/A2G. The F-15, on the other hand, is an amazing air-superiority fighter in its 15C format, and an amazing air-to-ground pounder in its 15E format, but those superlative abilities come at a higher cost.
However, the F-15 does have real advantages over the F-16, such as significantly greater combat range, a considerably bigger radar, FAR greater ability to carry more weaponry, speed (both climb and flat), altitude (can have an advantage in certain BVR engagements). The US, Israel and Japan use F-15s for air-superiority, even though they have F-16s (in Japan's case the F-16s bigger cousin, the F-2). There is a reason for that.
Bottom line - if you have the money the F-15 is definitely better than the 16. If you are on a budget and are out for cost-effectiveness, and you will likely be part of a coalition should a capable country attack you, the F-16 is the choice for you.