Since my sibling reply got voted up a lot, I want to follow up: it seems that not only is the question not wrong, the "dissolving" answer is itself wrong, or at least very misleading. (Naturally, I have to tread cautiously, since I'm not an Expert in this area.) As I said in my other reply, the defining characteristic of life is its ability to maintain a low-entropy island against the entropizing forces of nature. So there must be some range of environments in which an organism (via genes) is able to produce the same phenotype regardless of where its environment falls within that range. In effect, the genes allow the phenotype to be "screened off" (d-separated, whatever) from its environment (again, within limits). A thing that truly allows the environment equal influence in its final form as the thing itself (as suggested by the T&C answer) is not what we mean by "life". It's the hot water that eventually cools to a temperature somewhere between its current temperature and that of its initial environment. It's the compressed gas molecules in the corner of a chamber that eventually spread out evenly throughout the chamber. It is, in short, not the kind of self-replicating, low entropy island we associate with life, and so has no basic units thereof, be they genes or memes.

That sounds like less of a wrong question and more of a "right question with surprising (low prior) answer". As far as the asker knew, the answer could have turned out to be, "Genes produce the same organism phenotype across virtually all environments, so genes are more important because changing them is much more likely to change the expressed phenotype than changing the environment." (and indeed, life would not be life if genes could not force some level of environment-invariance, thereby acting as a control system for a low-entropy island) I don't see what's wrong with answering this question with "neither [i.e., they're equal], because they jointly determine phenotype, as independent changes in either have the same chance of affecting phenotype". An example of a wrong question, by contrast, would be something like, "Which path did the electron really take?" because it posits an invalid ontology of the world as a pre-requisite. The question about phenotypes doesn't do that.