I'd say, "That's alright, you really don't have to..." If they're like, "Aw, c'mon, a special treat!" I'd say, "Well, I mean, if you really want to, that's alright, but..."
That way you're not taking advantage of them but you're also not denying them making you happy.

when I go somewhere eating with someone else, it's often a battle of who's paying, and I think it wouldn't be different in such a case.
I would probably try to pay both meals just like always

So, if the person's just quicker in paying, I would be jokingly cheesed (while smiling), but thanking of course. If he would argue that he's earning more though, I would feel offended

What about just going halfsies? (I mean how much more expensive can the other guy's meal be right?)

I'd do like always. Once a friend and I went to the swimmingpool and she wanted to pay for me. I said she didn't have too. But she wanted and didn't mind.
So if people want to pay of kindness, not higher income, I let them.

Lol Ry - Ur polls are the only thing I come on to dA for these days...

If they say/insinuate that they make more $$, I'd refuse. If they just say, "Hey I got it this time", then yay, free meal

It depends on the person themselves. Such as, my relationship with them.
It also depends on the exact circumstances. I've gone out to places with my friends before and they've had to watch their budget and they worry about not having something to eat because they're a little low, and after some persuasion they let me pay for them. Most insist on paying me back, but I don't mind because me paying for them helps us enjoy our time together and they would do the same for me if they could. A couple even have done the same for me.

I have a severe problem with being payed for. I don't know why. I'd just rather pay it myself. I guess it's so that I don't feel like I owe them for anything.