FWIW, there's a two-part article on Clean Technica that details many of the differences between the two varieties of Mobile Connector:
In brief, as
@Misternt said, the Gen1 device can charge your car very slightly faster; but the Gen2 device is more technically advanced and
might be safer. (That's not to say the Gen1 adapter is unsafe in any absolute sense; but the Gen2 design seems to incorporate some more advanced safety features.) Furthermore, it looks like Tesla is abandoning the Gen1 device -- it's been out of stock for ages, and I seem to recall hearing that even recent Model S and Model X deliveries have been coming with the Gen2 EVSE. Personally, unless charging speed was of paramount importance, I'd go for a Gen2 Mobile Connector, along with whatever wall plug(s) I needed. If I had an LR Model 3 and charging speed was really important, I'd get a hard-wired Wall Connector, which can handle up to 48A, or a third-party J1772 EVSE that can do the same. (Not all J1772 EVSEs can provide 48A; in fact, that's a pretty rare feature. Most are 32A or less. Tesla's Wall Connector is probably the least-expensive 48A Level 2 EVSE.)