Every chicken has meat on it, and every chicken lays eggs. Whether raising a given breed is "worth it" depends on what you want out of the flock. If you want more eggs, laying breeds will more efficiently give you a greater number of eggs. If you want to emphasize meat, Jersey Giants or other traditional meat birds, or if you want to go there, single-purpose meat birds, will be a better fit. Until quite recently the idea of a chicken that was ONLY for laying or ONLY for meat was inconceivable and impractical. Both eggs and meat were collected at the appropriate times, as circumstances allowed and breeding demanded.
So my attitude is that any chicken is dual-purpose. "Dual purpose," "layer," etc are terms of convenience, not rules. The choice of breed just depends on what's most important to you. Example: I'm planning on phasing in a new flock of mainly Hamburgs this summer. Hamburgs are not conventionally classed as "dual-purpose" but they will serve as such for me, because I am looking for a chicken that eats more thriftily that the big "dual purpose" but still lays well, with meat and meat stock being a relatively less important (but still important) product from the flock. I've decided such a breed will most efficiently meet our needs. Trade-offs, always trade-offs.... There's no one right chicken otherwise there'd be only one breed.
