What do you do with them [MECH]?
To be honest: I am lacking the patience to play that long games. Either the war is lost or won before.
Nevertheless an interesting and complex question. (Splendid! Exactly the right thing for this peculiar emptiness I feel after 6 weeks of writing and thinking about the Naval guide and then suddenly... no more).
All 4 units: CAV-MOT-MEC-ARM, are the prime candidates for speed, spearheads and a good ratio for durability-combat power to man power (MP) usage.
Usually I try to tackle it by comparison.
Taken from the Germany 1942 scenario (DH full), all units available for research 1942, exception Arm-3 at 1943 but already researched by Germany in Nov 2942:
The picture is surprisingly mixed.
Speed, attack power, durability
First surprise: MOT is nominally the fastest unit by stats: 27 km/h, but is it really?
For simplicity assume day/night is half/half the time:
Cav-13: 23 km/h day, 6.9 km/h night => 14.95 km/h
Mot-3: 27 km/h day, 5.4 km/h night => 16.20 km/h
This is for plains, clear weather. If this is further modified by most other terrains and also most other weather, the difference in speed gets either neglectible or Cav-13 even faster.
MECH with a nominal speed of 22 km/h and in no weather or terrain the best, in 2 even the worst... somewhere inbetween.
ARM in many terrains and weather with good values but with the by far worst speed during night which devalues all boni and makes it the slowest unit overall.
If speed is the major factor: MOT or CAV.
Attack power: CAV, MOT, MECH have the same or nearly the same soft and hard attacks. No surprise, ARM with by far the heaviest hard attack.
Durability: Before looking at this comparison I would had thought the difference to be bigger. ARM with the best values, MOT with the worst (but still much better than for INF). All 4 unit-types very good candidates for a brigade that specifically lowers defensive and offensive vulnerability even more. Which would be a cheap AC for all. Alternatively for ARM, if you are willing to give up a bit of speed for an even further lowered softness: a medium-tank brigade.
Production costs: IC, time, MP
In 1942 the time to get any of those units will be probably quite crucial. So, first the normal production time and cost, followed by the upgrade times and costs from INF:
MOT-3: 189 x 10.80 = 2041 IC, 13 MP (upgrade from inf: 104 days, 1580 IC)
CAV-13: 213 x 12.60 = 2684 IC, 11 MP (upgrade from inf: 162 days, 1736 IC)
MEC-1: 207 x 14.17 = 2933 IC, 12 MP (upgrade from inf: 174 days, 2564 IC)
ARM-3: 207 x 21.64 = 4479 IC, 8 MP
In terms of cost and time it seems to be intersting to upgrade MOT and CAV from INF, not so much for MECH.
ARM can't be upgraded from INF but from CAV... which seems to make only sense if you have still very old cav-types (for example if you haven't researched the newer cav-techs a splendid way to transform old cavs into uptodate MOT, MECH or ARM).
If the speedy and cheapest availabilty of a fast unit is prime: an upgraded MOT from INF is the best.
Cost of an ARM rocks as usual thru the sky but with the least drain on MP. The latter double true because it is the most durable of all 4 units and thus the least receptible for damage and the corresponding costs of reinforcements in terms of IC and MP.
Fuel usage (TC-load)
Quite similar for MOT, CAV, MECH, escessive for ARM.
In the case of Germany: problems with MP and fuel and TC... a choice between pest or cholera.
Conclusion:
It is fine if you have MECH as units due to a scenario set up but I can't find a reason to go the extra way to research and build MECH.
Nor to spare a tech-team to research cav beyond 1932.
I do build cav and they are definetly not useless. And in above comparison I'd even say that Cav-13 is better than MOT-3. But early on, for cav to become competitive to a simple MOT-1 (1935) it needs a lot more time and research. Thus I usually upgrade my cav to the at that time even more useful MOT... or, if my MOT really need the support and under protest of the whining TC, to ARM.