I don't think the F-16s will be used for dogfights. Dogfights are fun in the movies, but in a real war, modern aircraft use missiles. The F-16 is just a platform for missiles and radar. And the US has developed many different missiles for the F-16, some with a very long range. For example, some variants of the following have a range of over 1,000 km.
https://en.wikipedia.org/wiki/AGM-158_JASSM
You can find the position of the parked bomber using satellites or ground observers, then you send the F-16 to fire the missile, and the bomber (or the ship, or the artillery) is no more.
No comparison with the MiGs. Yes, the F-16 as a platform was developed 50 years ago, but the weapons it carries are very modern.