If the installation is outdoors the Wall Connector is the better option, fully weather rated. The Gen3 Wall Connector now comes with a 24 ft charging cord (Gen2 was 24 ft, Gen3 was originally shorter. The Tesla Gen2 Mobile Connector has an 18.5 ft charging cord.) The Gen3 Wall Connector supports load sharing (up to 4 WC on the same circuit.) The WC can be programmed to only recognize specific Tesla vehicles (no free loaders using your WC.)This was informative as I am also new and was wondering the same question as OP. I was either going to have the electrician install a standard 14-50 outlet or do the Tesla WC as he was trying to talk me into that.
Seems like the miles charged per hr would not be a deal breaker from a WC to the plug that comes with the car using the adapter to charge at 14-50. The only real benefit of spending the extra $550 is the cool factor but not much more if the added miles don't matter.