I’m trying to decide which “wall connector” to install in my garage. For the beginning I’ll be using the portable cable that comes with the car connecting to a 6-50 outlet I have in my shop for welding. Long term I’ll likely install something in my house garage to make things more convenient. Question is do I buy the Tesla unit for $500 or something more generic that just comes with a standard J1772? Since the car comes with the J1772 adapter why not get a more generic charging connector ? What’s the advantage to the T branded unit? I have no issue going either route.
The main advantage of the Tesla Wall Connector is that it comes with the Tesla plug, so you don't need an adapter. This is mainly a convenience issue, since having the adapter attached makes using a J1772 plug a little more awkward -- a J1772 unit won't open the charge door when you push the button (but tapping the cover opens it, so this is a very minor point), and it's a little bit easier to unplug Tesla's plug than a J1772 with an adapter attached. These are very minor convenience issues, though. A slightly bigger one, IMHO, is that using a J1772 EVSE means you'll need to buy a dedicated J1772 adapter to keep permanently with the EVSE, thus raising the cost; frequently unplug the adapter from the EVSE and store it in the car, which is a bigger hassle and increases wear and tear on the plug and adapter; or
not routinely carry the J1772 adapter with you, which will make it impossible to charge at most public Level 2 EVSEs. One more point is that any electrical adapter or connector is a potential point of failure. There are reports here about J1772 adapters that have melted because of problems, which
might be related to insecure connections. If the EVSE is mounted outdoors, or if you run the cable outside to charge, there's greater chance of water seeping into the connection and causing problems. Finally, Tesla's Wall Connector is reasonably priced -- $500 is about as low as you'll find third-party EVSEs capable of 32A or better charging (and Tesla's will charge an LR Model 3 at 48A), so you're getting the advantages of the Tesla adapter and not paying any more money for it, unless you find an unusually good deal on a J1772 EVSE.
The main advantage of a J1772 EVSE is that it can be used with other vehicles. If you already have or plan to add a non-Tesla EVSE or if you expect to have friends visit regularly who want to charge, then a J1772 EVSE may be worth considering. (There are adapters to let cars with J1772 ports charge from a Tesla Wall Connector, but they cost ~$250, vs. $95 for Tesla's J1772 adapter to go the other way.) Another advantage of
some third-party EVSEs is that some of them have features not found in Tesla's. A few manufacturers, like eMotorWerks and ChargePoint, make Internet-enabled EVSEs, which may be desirable if you're a data junkie. (OTOH, you can get much of the same data from the Tesla via its API or a service like TeslaFi.) There are a few minor oddball features on some EVSEs, too, like delayed charging (but this doesn't always work well with Teslas, and is a feature provided by Tesla vehicles, too) and readouts that display basic data like voltage and amperage (but again, you can get that from your car). It's also conceivable you'd prefer the styling of a specific third-party EVSE.
Overall, if you don't anticipate the need to charge non-Tesla vehicles, chances are Tesla's Wall Connector would be the better choice unless you get a
really good deal on a third-party EVSE -- say, $300 or less on a unit that can deliver at least 32A, and preferably more. The biggest reason to buy a J1772 EVSE would be if you need to charge non-Tesla EVs, either now or in the near future.
Of course, if you're looking for the least expensive way to do it, that's to use the portable EVSE that comes with the Model 3. They used to ship with NEMA 14-50 plugs/adapters. Those are no longer included, but can be bought for $35. Thus, installing a NEMA 14-50 outlet, hanging the included EVSE on the wall, and plugging it in gives you 32A, 240V charging for $35 plus whatever the outlet costs, saving you perhaps $400 (or more, if you've already got the NEMA 14-50 outlet) over the cost of the Wall Connector. Personally, I'd be fine with this if I had a reasonably secure garage; but if I wanted to mount an EVSE outside, I'd prefer something that's hard-wired and bolted to the wall, rather than plugged in. Having a separate, permanently installed EVSE would also make it slightly better for road trips, since then there'd be no need to stow the EVSE in the car before the trip and then re-hang it on the wall afterward. That's likely a very minor factor unless you go on a lot of road trips, though.
FWIW, I use a Clipper Creek HCS-40 with a JuiceNet board installed. I use this EVSE because I bought it for a Chevy Volt that I drove prior to buying my Tesla Model 3. It was easier and cheaper to buy an extra $95 J1772 adapter than to replace the EVSE, so my case falls into the "need to charge non-Tesla EVs" category, albeit temporally displaced. I've charged with the portable EVSE that comes with the Tesla a few times just to figure out the details of using its plug, and so I can say from personal experience that its advantages over a J1772 with adapter are quite minor. If I needed to replace my Clipper Creek for some reason, I'd probably replace it with Tesla's Wall Connector.