Your genset should be big enough to power your a/c unit. Normally you'd want at least a 3000watt model....with the modern ones that'd be an EU3000.
I have known guys to run theirs' with an EU2000, but they have a large start capacitor in the a/c unit to build up the "oomph" to turn it over.
So the question I'd have for you is: Do you have an extra large start capacitor that you put in? Or is it bone stock?
You won't want it to run on wide open all night long, as your a/c will probably cycle in and out. You might be fine as-is with a 3500 watt genset. I would think that you would be, if it works OK. But if you're worried about it, get a big capacitor for the a/c unit and wire it in.
Is your old 3500 a loud one? If so, are you camping out in the boonies away from other folks? A lot of people get mad if a "contractor generator" is running all night, that sounds like a Bell Huey hovering over the campground. But the inverter type generators that are really quiet you never hear anybody grumble about.
You'd probably be AOK to just run it on "eco" mode with your a/c as-is. But if you have time to put in a big start capacitor, I'd go for that.
Me, I've only got one EU2000i and the a/c is bone stock, so no a/c for me on the gennie. I meant to buy a second EU2000 with the parallel kit, but just haven't gotten around to it.
Best of luck,