Yes, the CA may well read differently with different types of controller, as it's current calibration is determined by the value of the shunt resistor (if it's using the internal controller shunt).
Here is the section from the CA manual that covers this:
"Set RShunt:
The Cycle Analyst is calibrated by programming a resistance value for the
current sensing shunt. If you are using a known shunt resistor, then as a first
estimate this value can be programmed in mOhm. This will usually get the meter
accurate to within 3%. For highest accuracy, the shunt value should be calibrated
so that the displayed amperage matches that of a known current reference,
which may not be exactly the same as the mOhm rating on the resistor. If the
current is reading too low, then the shunt resistance value needs to be
decreased, and visa versa. Stand Alone Cycle Analysts, and Direct Plug-in units
that are sold at the same time as a controller, are all pre-calibrated to the shunts
with which they were sold.
Allowable values in High Range mode: 0.728 to 9.999 mOhm
Allowable values in Low Range mode: 0.0728 to 0.9999 mOhm
If a shunt value is input that falls below this range, then it will be reset to the
lowest permitted number. "
If you purchased your controllers at different times, then it's possible that the CA may be correctly set for the 20A one but not for the 35A one.
As already advised, I'd do a quick test with an ammeter just to see if the CA current readout is correct when it's hooked up to the 35A controller.
Jeremy