We have an environment with UCS blade firmware about 1 year old and ESXi at 5.1 Patch 6. Upgrading to Cisco Custom ESXi 5.1 Update 3. What order would you do first, firmware on the blades then ESXi or visa versa? Both should be OK but just wondering.
i would suggest you to first upgrade the firmware of your host and after that go for the host version upgrade.
It's more about making sure that your hardware firmware level are suitable with new upgrade that you are planning to do.
I would ideally begin by updating firmware first if current level is not suitable for upgraded version of ESXi
Please see following KB