Fossil fuel generators vs battery

This survey that @Dcdyer posted regarding Home & Portable Generators has made me think about those who want to migrate from fossil fuel powered generators to a battery system. And likewise those (myself included) who want to get a backup system and are confronted by the pros of fossil-powered (cheaper; “infinite” runtime) vs cons of lithium (expensive; limited runtime) and the cons of fossil (polluting, dangerous, ugly transfer) vs pros of lithium (elegant transfer, grid offset, load-shifting for grid TOU and solar, “safe”).

A home backup battery can perhaps be thought of in terms of an EV. In a pinch, a house without a battery can use Vehicle to Home (V2H) power. In a worse pinch, you can drive away or even recharge your battery (and so house) from your hybrid. I guess there’s also the interesting possibility that if you have a fossil generator anyway, you can charge your house battery and/or EV using it!

So then the question becomes, if you are going to buy a car and a backup system what do you do and how do the costs shake out in the real world?