Did you change pinouts, hardware configurations, etc. for switching between the two modules?
By same firmware, I assume you mean the same *.c files as well as the same components?
Giving the errors/responses from the CySmart upon connection attempt would be helpful; Also, if you can post a minimal-bundle-zip-archive of your project so we can check hardware settings etc, it will help for us to see what the file settings are :)
Did you update the dongle to the latest firmware for CYSmart 1.2 Hex file?
Can you please try setting ECO cap trim value for CYBLE-212020-01 as suggested in following KBA and try?
For setting ECO capacitance trim value in firmware, add the following code in the CYBLE_EVT_STACK_ON event:
CY_SET_XTND_REG32((void CYFAR *)(CYREG_BLE_BLERD_BB_XO_CAPTRIM), 0x0000BCBC);
I tried setting ECO cap trim value and now it's working fine! That was the stuff.
Thank you all, specially thanks to Anjana!