I honestly have no idea if this is considered fallacious or not, but for some odd reason...
This is a strong indication that at least in some contexts, we are talking about a paradox rather than about a fallacy. The fallacy of relative privation ("not as bad as") is listed under the red herring fallacies on wikipedia, i.e. it is a fallacy of relevance. So if the bigger problem is not really relevant in the context of the smaller problem under discussion, then it is indeed a fallacy.
An unpleasant variant of this fallacy or paradox if the time and resources for the discussion the problem(s) are used to draw a relation between the unrelated problems. This form of the paradox can indeed happen in practice, take the principle of explosion in logic, which allows to deduce anything from a completely unrelated contradiction. A denial of service attack on a server highlights that even systems designed to guard themselves against this sort of unpleasantness are not completely immune to it.
For instances of the paradox where the bigger problem is really relevant, the marginal return might help explain why sometimes the small problem promises a bigger payoff than the large problem for the same amount of invested resources. Again in the context of logic and computers, floating point numbers will forget small numbers, if they are added to big numbers. The remedy here is to try to separate different scales before putting them through black box algorithm.