EU 1000 - my choice
First of all, I'm fulltiming, single and will spend most of my time at full hookup facilities, so my need for any generator will be infrequent.
Second, I like the light weight and low cost of the EU 1000. I can lift the 1000 without any strain and it will carry nicely in the back of the Suburban. If I do boondock or go through a power outage, I'm ready to deal with being without A/C, but I don't want to be sitting in the dark for hours. I could probably warm my 22ft with my hairdryer! I've got a gas tow vehicle with a 38 gallon tank - and a syphon. That eliminates needing to carry a gas can and another 10 minute delay for inspection at every tunnel. In Tidewater it's hard to leave without going thru a Tunnel!
Third, solar - well a solar panel's performance isn't good on a shady sight, or if your panel is oriented other than in a southward direction. If you can't park your A/S so that the panel is on the south side, I suspect you'll be getting a trickle of power. For ideal performance you need to know the angle of the sun which changes significantly between say Maine and Florida, and raise the panel so that it's getting rays at as close to straight on as possible. I've only seen two Airstreams with solar panels and they were on a fixed mounting. I've seen a ground mount unit that rotates and allow you to crank the angle up and down, and I suspect that a roof mount could do the same (ah, another lock down hook like the Zip Dee awning to check before you hitch up and go).
I'll stick with the itty-bitty generator for now.