V2H - charger inverts DC to grid AC

V2L - EV inverts DC to grid AC

In case of V2H it therefore doesn’t matter what supported EV you are using, rather what charger you are using.

In general for changeover during a black out, V2L is probably better, because with V2H the charger itself needs POWER to boot up and request V2G whereas V2L you can start from the EV itself.

Also, generally speaking V2H is designed to be grid-following and certified to half a dozen standards whereas V2L forms an isolated microgrid, and a lot of the rules are tossed out, which is what you want.

For V2L you just need a generator changeover to isolate your house from the grid (most commonly just a manual switch), and a reverse plug to connect EV output to switchboard input.