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deschutron comments on Stupid Questions February 2015 - Less Wrong Discussion
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I just read a description of that lottery. I see its expected value is a divergent series. If both games you compare have their expected values defined this way then I think you can subtract one series from the other. i think this is the approach you mentioned, and I would do it.
Also, I'm not an expert on infinity, but I think there are different kinds of infinity. If one game gives you, on average, a dollar for each natural number, and one gives you, on average, one dollar for each pair of natural numbers that exists, then the second game gives you infinitely as much expected value as the first one.
Equivalence of infinite cardinalities is determined by whether a bijection between sets of those cardinalities exists. In this case, if interpreted as cardinalities, both infinities would be equal.
Also, the order in which you sum the terms in a series can matter. See here: https://en.wikipedia.org/wiki/Alternating_series#Rearrangements