The F-104 is the design contemporary to the MiG-21 but primarily industrial differences between east-west led to the F4 being the primary Fishbed contemporary between US/USSR. In terms of progression the F-104 and MiG-21 entered service almost alongside each other and have similar performance, and are both day fighters, etc.
The MiG wasn't designed for export, or as a light fighter concept in any way reminiscent of US Freedom Fighter or LFX requirements. Its design philosophy was as a main type for Frontal Aviation as opposed to PVO-Strany, which means operating from rough forward fields with easy and cheap mass production, high turnaround, low maintenance and within range of ground based Army support. The Israeli comparative report (they were the first in the west to get hold of one and flight test it), was that it was cheap and uncomplicated, performance exceeded expectation and it was the most maintenance free jet they'd ever seen up to that time.
Secondarily this aircraft type was to be distributed among satellites and later was offered for export. That's the role of major Frontal Aviation fighters. It's really all about production philosophies and resource expenditure, not aircraft type.
The US industrial philosophy was entirely different, so if the F4 was produced in the USSR as quickly as it was in the US, of which the MiG-23 is a rough contemporary (ie. of the F4E/N) then it would've been issued to PVO only, who has a much bigger "budget" to work with. The Su-15 for example is a more expensive and more refined contemporary of the MiG-21 and century series fighters, and would match up much better with an early F4 at low alt but it was issued to PVO, their national guard equivalent.
So for a technological contemporary for the MiG-21 you're really looking at the century series fighters (the MiG was in service from 1958) but for actual mission building contemporaries I agree the Mirage III and F4B/C are the best choices. Later Phantoms are inappropriate however, if you model their improved avionics. Early Phantoms with no lookdown and crappy target discrimination should be used, with missile problems and better success rates using gun pods. Anywhere near the ground or against clouds or in the direction of the sun, or in formation or during rough manoeuvres the radar on early Phantoms is just about useless in combat. Those early ones fought mostly like day fighters with really good thrust excess mostly, and just salvoed their weapons and hoped for the best. The second crewmember wound up being an observer, both crew spend all their combat time "eyes out" of the cockpit.
Israeli pilots who operated Mirage, Phantoms and Eagles said the Eagle was the first fighter you could spend time during combat with your eyes on the radar screen instead of out of the cockpit, but the other types were all old school and not very different from each other in that respect.