I dont believe the rivalry is between Superchargers as most chademo is ~25 KW and as such it competes more with the HPWC, and High amperage J1772. Part of the competition is that it costs much more to install. I'm not against it, but the numbers make it less attractive.
I don't think even a large minority are 25kW. All the Nissan branded ones are 44kW. The rest are mostly 62.5kW (500 volts * 125 amps), however a LEAF, Tesla Model S, or any of the other 400-ish volt cars will only pull the maximum 125 amps max * 400 volts = 50kW.
A few other facts to consider when comparing to Supercharger. Those don't operate with two cars on one charger (the "A" and "B" stall) at 120kW each, but instead some number for each car that totals 120kW. So, it's easy to imagine one car on CHAdeMO sucking down 50kW and the Supercharger only getting 60kW.
Finally, all the DC quick chargers are the same when the battery gets near full and starts slowing the charge speed.
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The largest portions of cost are the charging station itself and 480V transformer at ~$23k and ~$17k. Next up is labor, which would primarily be trenching/etc costs.
Tesla uses 500KVA transformers for the four 120kW Supercharger station (7-8 stalls). It's not much more money than the far smaller ones:
Reconditioned Price: $26,425.00
Product: Oil Transformer
Manufacturer:
Stock No.: 11-4159
Phase: 3
KVA: 500
Primary Voltage: 22860/13200
Secondary Voltage: 208/120
Taps: 2+2-
Temp. Rating (ºC): 65
Impedance Pct.:
Serial Number:
Description: Oil Transformer, Stock No. 11-4159, 3 Phase, KVA 500, KVA 500, Primary Voltage 22860/13200, Secondary Voltage 208/120, 2+2- Taps, 65 ºC Temp Rating, Impedance Pct., Serial No. , Reconditioned Price $26,425.00