It is a design choice as the intended missions of both aircrafts differed slightly.
The inlet of the Eurofighter Typhoon features variable geometry, to improve the performance at high angle-of-attack and performance at transsonic and supersonic speeds. This design choice was made because the Eurofighter Typhoon is intended to be used as a top of the line, hyperagile aircraft which outstanding dogfight and interceptor performance. The twin-egine design, canards, relaxed stability/unstable design and the originally envisioned thrust vectoring engines were to help in this mission profile. The expensive and complex variable geometry inlet is therefore only a logical choice when you put in other equally complex systems to enable this use profile.
The F-16 on the other hand was designed to be relatively cheap, easy to maintain and to have a low operating cost. This was partially achieved by installing only a single engine with a straight inlet and no complex variable inlet duct. The disadvantage in the transsonic and supersonic regime as well as drawbacks at high angle-of-attack were accepted in order to keep the aircrafts cost low. Other fighters such as the F-15 or F-22 should fill the role of higher-cost aircraft.
See also this post about the inlet of the F-16.
In hindsight, the F-16 has obviously aged better. The Eurofigher Typhoon while being remarkably agile, probably the most capable Dogfighter ever, has never been in a real dogfight (at least to my knowledge). Instead, missiles have taken over this aspect of air-to-air combat. The F-16 on the other hand is a very cheap still very capable aircraft which is cheap to operate while it still can execute todays mission reasonably well. The Eurofighter can fullfill the same mission, however operating costs are significantly higher.
P.S. Do not get me wrong, the Eurofighter is a remarkable piece of engineering. Especially the flight control system is an absolute beast!