Many archers looking for a bow also shoot vertical bows, most of those are compound bows. So, when looking for a bow, they may not consider a recurve bow. However, both styles offer advantages, and it makes sense to consider your needs and mechanical issues when deciding.
When it comes to using the bows, perhaps the biggest difference involves drawing the string. With a compound bow, the let off occurs at about 50% pull, as the cams and cables do their work. There is no let off with a recurve, so the archer must pull all the way to the trigger lock. If you are using a bow due to physical limitations, this may be the deciding factor. But do keep in mind that if you prefer a recurve for other reasons, foot stirrups may provide the help you need in cocking the bow. In ease of use, recurve triggers are typically about 3 lb pulls, while some compound models have pulls in excess of 6 lbs. If hand conditions are a factor, take a look at that spec when considering your selection. In ease of use, compound bows offer a slight overall advantage. One additional note: Compound bows are also slightly more narrow than recurve bows, providing a more compact, although slightly heavier, package.
When it comes to reliability, recurve bows step to the forefront. The key factor is that their simple design employs fewer mechanical components, and therefore, suffers fewer mechanical breaks and malfunctions. On compounds, wheels/cams may come loose at inconvenient times, or a cable may break, ending your archery day, or possibly even causing injury. These are rare occurrences, to be sure, but they never happen with a recurve, and for that reason, their simple design gives them the advantage in terms of mechanical reliability. It also helps that string changes are easier with recurves.
One additional note: with fewer mechanical parts, recurve bows are slightly quieter on draw and release.
Beyond these factors, modern recurve bow manufacturers offer models that are just as powerful, fast, and accurate as most compound bows, with velocities of 265 fps to 300 fps very common. The bottom line is that both styles make for fantastic archery. You cannot go wrong, either way.
The top recurve bow manufacturers are: Bear Archery, Diamond, Hoyt, Martin Archery and PSE and the top compound bow manufacturers are: Bear Archery, Diamond, Martin Archery and PSE