you might want to actually keep and reuse your current C6.
the big difference is in the ports for the trans cooler lines and the shift selector for the valve body.
you can get a 71-73 selector and install it in your current transmission matching the original linkage that the car would of had if it was born with a c6.
FMX and C6 are different but kind of work if you fudge it on the shifter linkage.
usually with the cooler lines you can install adapters and fudge it so it works with the reproduction lines and the original Radiator trans cooler.
reasons to keep a late model trans:
more clutch plates and steels. the original 71-73 C6 is actually pretty weak it has 3 clutches in the forward and direct drums and then 4 on the main body.
later model transmissions had 4,5,6,even 7 clutches.
to do this on a original transmission case requires a machine shop and a lot of work to beef it up. you can swap later model drums into the original trans like i did.
there are some good parts in the the older transmissions that are better like the roller cage on the original is steel, and plastic on late models.
nothing really wrong with the plastic ones unless you plan to really hammer on this C6 transmission drag racing and burnouts all the time.
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anti clunk design
this came after 1977 a late model will have this, it can be good or bad depending on what you are planning the best is you can take out the anti clunk spring washer and make room for even more Steels and clutches making the transmission stronger.
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drum piston seals. ford changed the design on these after 1977 there are also more drains in the newer transmissions verse the early ones, the old trans tend not to drain down when the car sits and going into gear the first time it clunks or snaps into reverse and people thought the trans was messed up so ford made some changes to try and soften a first morning cold start shift into gear. again racers want the trans to not easily drain down verse the normal guy that wants a nice smooth shift.
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otherwise functionally the transmissions are the same outside of the different shift selectors for the valve body you can beef up either old or new with aftermarket but a lot of guys start with a later model transmission then swap in a couple older parts to make it better.
Servos and levers also make a difference higher performance C6 transmissions have better levers and servos but you can again swap these with new production performance parts.
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just letting you know what you are in for.
i had a 1977 C6 which was not worth repairing and got a 1972, 1973 and a late 1980s C6 to mix together to create one good 1973 type transmission with correct selector linkage.
http://www.7173mustangs.com/thread-the-curse-of-the-blown-transmissions-strikes-again
i upgraded mine a little to make it better as well.