Which will become widely available first? Organs grown in clone farms, or artificial organs? I'm thinking more about kidneys and lungs than simpler organs.
Considering the state of the art, we have BOTH. We already grow skin (which is an organ). We also have artificial skin of sorts, but that's largely a scaffold for encouraging real skin to grow. We have enough artificial parts going around to qualify for very simple organ replacement. However, you're right: we can't replace a kidney or lung. In fact, we can't replace any of the organs or structures.
Overall, by downgrading your expectations of what's an "organ", artificial organs should arrive first. I say this because not only is biological development rather infantile in that regard, technological miniaturization can shrink external equipment into attached or implanted solutions. For example, we do replace kidneys with dialysis, but dialysis equipment is shrinking ... and eventually can become more internal and combined with a home unit that is var more convenient. Every day you could then attach yourself via implanted connectors to your home unit and "dialysize" yourself ... holding down your costs and producing a much better lifestyle since you can flush wastes from the blood more often (since in normal folk the kidneys filter the blood constantly).