NRF24L01+ not communication
The 3.3 V LDO on the Nano is in the FT232RL USB/UART chip and is rated to only 50 mA maximum external current. Drawing more current than it can supply will corrupt all data in the USB channel so I'm not surprised you get corrupted data when you connect the power module boards. 

The NRF24L01+ modules you call model A have a separate RF power amplifier on them that draws peaks of 250-350 mA and will NOT work connected to an Arduino Nano as shown. (I have both types of modules and see no operational differences between them other than the external power supply for the larger module)  

These high power modules need to be powered separately with their own 3.3 V regulator.
I can only assume you wired the modules incorrectly to an external supply.  

There are readily available small 1117-3.3 based regulators (800 mA), and you might read here for help on those.