Either method will work, just use your best judgement. IMHO, the more control you have over the upgrade process, the better. Storing the firmware locally removes any dependencies on the Internet. Using a wired connection, further removes any dependencies on maintaining a persistent wireless connection on your LAN.
In either case, if you choose to upgrade your firmware, (1) make sure the power connections to the network camera, router, and host PC are well seated, and (2) if you are using a wireless connection, make sure the signal is strong enough to support the file transfer.