Drivers are on the ESXi side while firmware is on the hardware side and thus generally require plug-ins from the hardware vendor to check these, thus why these would need to be used for accessing this information from the CLI, for example on older hpssacli:
# /opt/hp/hpssacli/bin/hpssacli ctrl all show detail
However for some driver-families it is possible to determine controller firmware from other locations, for example lsi_mr3 lists the controller firmware in the ESXi boot log (/var/log/boot.gz) - note that other driver-families such as lsi_msgpt3 (and also depending on version) can print unreliable base information here e.g it will state 11.00.00.00 when it is using 11.65.05.00 .
Other times you might be able to get package/BIOS versions from boot log which one can correlate to firmware versions from what these contain.
There are a few other side-way approaches to get this information but best approach is to just check from the out-of-band-management or from vSphere if you have the necessary 3rd-party plug-ins (if they exist).
You can tell firmware version ('Revision') of the disks from esxcli:
# esxcli storage core device list