Always make an NVM backup before upgrading firmware. The ZHA integration does this automatically but if using a ZBDongle-E with Zigbee2MQTT then currently suggest temporarily moving the radio adapter to a other computer and perform a manual backup with zigpy-cli https://github.com/zigpy/zigpy-cli
If you are using the ZHA integration then it does not matter, both ZBDongle-E and ZBDongle-P work great there and have feature-parity in it (all functions/features works equally well for those in ZHA).
If you are using Zigbee2MQTT then the ZBDongle-P is recommended because it is based on a CC2652P radio SoC as it uses Texas Instruments Z-Stack which has been supported since the inception of the zigbee-herdman library that Zigbee2MQTT depends on and thus support for it is more mature in its code.
The support for ZBDongle-E (based on an EFR32MG21 radio SoC) which uses Silicon Labs EmberZNet (EZSP adapter) is still very good in Zigbee2MQTT’s zigbee-herdman library but support for it is newer there and therefor does not yet have feature-parity (most importantly it is missing full backup and restore features in Zigbee2MQTT).
Because of this, if you are using the ZHA integration then it is really easy to migrate back and forth between ZBDongle-E to ZBDongle-P and vice versa, (just click on “migrate radio” in the ZHA integration and follow the instructions), however, if you are using Zigbee2MQTT then it is much more complicated process to migrate from ZBDongle-E to ZBDongle-P or vice versa (reason being that missing full backup and restore features in Zigbee2MQTT), however it is possible to work around that using third-party tools for backup and restore for that see this zigbee-herdsman discussion here → migrating coordinator from ZBDongle-E to ZBDongle-P · Koenkk/zigbee2mqtt · Discussion #16478 · GitHub
Regardless, I recommend upgrading the firmware on both adapters before performing any migrations.
If you bought a ZBDongle-P and newer upgraded he firmware then the recommendation is to upgrade it, it is really easy as long as you just stop your Zigbee gateway application and unplug the Zigbee Coordinator USB adapter to perform the firmware upgrade on a different computer with desktop OS. anyway, for ZBDongle-P, see → ITead's "Sonoff Zigbee 3.0 USB Dongle Plus" (model "ZBDongle-P") based on Texas Instruments CC2652P +20dBm radio SoC/MCU
If you are using ZBDongle-E (which this thread is about) then suggest staying with the 6.10.x firmware which has proven to be very stable and only if you are having issues with some new device should you consider upgrading the firmware to the latest 7.3.x firmware which many people have also reported as stable. As long as you make a backup before upgrading then you can always restore that.
While the ezsp adapter support remains in Alpha/Beta stage for Zigbee2MQTT I suggest that you post such feedback directly to zigbee-herdsman ezsp adapter developer(s) here as that is what Zigbee2MQTT (and IoBroker) depends on → [WIP]: EFR32 EZSP adapter implementation and test · Issue #319 · Koenkk/zigbee-herdsman · GitHub