Using AT+WBHV=1,1 requires that the module be restarted and prevents further access to SIM commands, while AT+CFUN=4 only turns off the GSM stack and keeps access to SIM commands and don’t require any restart.
In the Working Modes section there is no mention of the specific case I asked about, and even in the PTS document, the power consumption figures indicate that the power consumption is higher with GSM stack off than with it on.
The difference is small enough to not matter much, but it doesn’t seem to make any sense that power consumption is slightly higher with stack turned off.