A few years ago, there was a post asking about the design philosophies behind Cold War submarines. Was there a similar difference in design philosophy between the Americans and Soviets when it came to designing fighter planes? Or were they going after the same thing with, say, the F-4 and MiG-21?
A similar question was asked a few years ago and answered here by. In summary, Soviet fighters were generally less complex and less expensive than equivalent Western fighters. It's debatable to what extend this was due to Soviet technological limitations versus the Soviet desire to market aircraft to countries which could not afford to buy and maintain more expensive and complicated Western aircraft.
You ask specifically about the F-4 and the MiG-21, so I'll compare those two. Both the F-4 and MiG-21 were very widely used, popular aircraft. The differences between them illustrate some of the general themes of American and Soviet designs.
The F-4 is much larger, with a two-man crew and a powerful radar. These features allow the F-4 to be an extremely versatile aircraft, and some engineers have half-jokingly said that the F-4 was a "solution in search of a problem" for most of its career. The enormous size allows the F-4 to carry a wide variety of weapons, so it can perform numerous different tasks. The second crewman takes some of the burden off the pilot, allowing the use of sophisticated and complex weapons systems. On the con side, the F-4 is a very expensive aircraft to buy, operate, and maintain. Relatively few countries can afford to buy and use them effectively. Plus, some of the features that looked good on paper have proven detrimental in combat. This was especially prominent during the Vietnam War, when the very sophisticated and powerful F-4 struggled with close-range combat against lighter, smaller, more agile opponents.
In contrast, the MiG-21 is a small aircraft with a one-man crew, relatively simple instrumentation, and a short range. This meant that almost any country that had good relations with the Soviet Union could afford to buy MiGs, train pilots, and operate them for a long time without breaking the bank. The MiG-21 was an enormous success on the export market, being the most-produced supersonic aircraft ever made. It is still in active service for 18 countries (in contrast, the F-4, which ended production in the same year, is currently in service with only 4 countries). However, this simplicity also came with trade-offs. The Mig-21 has a very short range and a limited ability to carry munitions, which hampers its ability to be an effective combat aircraft in any role except point defense.
The F-4 was a big, powerful jack-of-all-trades which was limited by its cost and complexity. The MiG-21 was a small, light interceptor which was less versatile but very accessible to anyone who had a few airstrips and a few dollars.
Some sources:
https://www.boeing.com/history/products/f-4-phantom-ii.page