It kind of depends. How much control do you have over your actions? If we're going MHI style vampires, you're basically gone; once you're a vampire you are completely subsumed by it, and you (or at least your body) pretty much become evil. In that case, you'd not be able to commit suicide even if you wanted to (or, alternatively, your sense of morality would be warped so you wouldn't want to).
If you were more like Blade/Angel/(possibly)Supernatural vampires, and were able to somewhat control your actions, then you have more options. If you can control your cravings and/or pick your targets, there is something to be said for becoming a vampiric Punisher, or perhaps a Blade/Angel-type vampire who hunts down other monsters that aren't so picky. OTOH, if you can't control your cravings, and you pretty much loose your *expletive deleted* whenever you're around normal humans, then yeah, suicide becomes pretty attractive at that point.