Mirages and MiGs swap

Or - people at MiG make a delta-wing Mach 2 fighter by late 1950s/early 60s instead of MiG-21, then an 'classic' layout fighter like it was the Mirage F1 instead of the swing-wing MiG-23, and an up-to-date 1-engined delta-wing fighter in the early 1980s. In the same time, Dassault makes the MiG-21-equivalent instead of a delta-wing fighter, then they do a bigger, swing-wing fighter by the 1960s/1970s, and then a 2-engined 'classic' fighter by the early 1980s. Mirage 4000 does not happen, while Mirage IV or equivalent does. MiG still makes the -25 and -31. Both companies use domestic engines, electronics and weapons in the process.

What changes in some of aerial battles we can expect? Commercial success change, both at home and abroad? Financial 'health' of the respective companies by late 1980s/early 1990s? Upgrade-ability past 1990? Further developments in respective companies past 1995-ish?

You have created another interesting thread!

I doubt that much would change. The Mig 21 and Mirage III/V were close in performance with similar pluses and minuses with the Mig 21 having the advantage of better agility.

The main difference was the training of the aircrew which doesn't really change

MiG-21 was not as capable as Mirage III or V as a 'payload carrier', ie. combined weapons + fuel carriage was not as good. Might curtail some Israeli operations, like the long range bombing runs undertaken during the war of 1967. OTOH, Vietnam air war will go as-is, the Mach 2 fighters were used in low number by North Vietnam, even if to a good effect.

MiG-23 vs. Mirage F1 swap - the western-leaning countries have an even greater 'exposure' to the swing-wing technology. Hopefully the French will be doing a better job than MiG at making the wing box sturdy enough, that historically needed two redesigns so it can withstand high G maneuvers. Conversely, the 'Soviet F1' gets a much better commercial success abroad, being a much simpler machine to make and maintain, thus less taxing on government's budget. India licence-builds the type. China makes a 'solid nose' J-7 by early 1980s.

Soviet 'MiG-2000' is probably seen as a true replacement for the fighters conceived in 1960s, unlike the historical MiG-29? Meaning that Soviet-leaning countries make a faster switch towards the new-gen stuff in the 1980s, than it was the case historically. Halving the number of engines to fuel and maintain (vs. MiG-29) should've keep the fighter serviceable and upgradeable between 1990-2010 even with smaller military budgets. No carrier-borne version. Iraq buys them in great numbers.
The 'Mirage 29' might've seen a good deal of use in hands of French AF, as well as in Greece. French will be pressed to make a long-range version of it, somethning like the later MiG-29 versions, from the -M onwards. Possibly no export to India due to price in 1980s, where 'MiG-2000' is bought in great numbers instead? French develop the naval version for them, that might suit Indian needs instead of the existing MiG-29K?