It's a misnomer and an oxymoron to say that someone is in "bad health." Disease is not a state of health but an abrogation of health. What we refer to as "good health" is, in fact, the normal state of life. Since human flourishing is the standard by which we judge the good, then deviations from it are necessarily the exception--as it would make no sense to hold a baseline standard that was not the norm. This principle is easy to demonstrate in physical well being. A man who has the flu is not a flourishing human being. He lacks health momentarily but soon returns to a satisfactory equilibrium. He regains his health. The more complex example is to compare an ordinary, non-diseased man with another who also happens to eat well and exercise. Are both men in good health but with different degrees of good? No. The latter man, assuming he understands himself and the basics of nutrition, is healthy while the former man is probably in a slightly unhealthy state. He certainly isn't healthy in the proper definition of the term.
Admittedly, it's a different way of framing the issue than most people are used to, and some people, I'm sure, would disagree. But even among the people who agree with me, there are relatively few who view happiness the same way. Yet, using a flourishing life as your standard, I contend that happiness (rationally self-interested happiness) is "health," and unhappiness is the absence of "health." As such, it's important to view unhappiness as a fleeting aberration, as a disruption of what is proper for a human--in the same way that a cold interrupts physical well being. Many people are too quick to accept that unhappiness is a normal state of being. This makes little sense. If given a cancer diagnosis, most people would (I hope and assume) fight the disease to the best of their ability, never conceding that cancer is an acceptable state of health or, worse yet, that it is health. Yet this is exactly how some people view unhappiness: as a form of living or as life itself.
In the same way that disease is not health, unhappiness is not life. I mean this in as close to a literal sense as I can convey without being a literalist. Unhappiness is the absence of life. To maintain a state of unhappiness--that is, to accept it as living--is equivalent to accepting the flu as health and refusing to treat it. In both cases, the disease may go away on its own. Or, as sometimes happens, the disease kills you--metaphorically, literally, a combination of both.
I, for one, choose health. Do you?