SOHC and DOHC simply mean that the SOHC has a Single OverHead Camshaft, while a DOHC means Double OverHead Camshaft. The power and fuel efficiency really depend on what kind of tuning the engines were designed for, because there are cars that have DOHC engines but are meant for fuel economy, while on the other hand there are cars that have SOHC engines that can be tuned for much more power.

In stock form, typically the DOHC will have more power gains due to better control of the valves, since there are two camshafts. More power results in increased fuel consumption, but a better (meaning, lower) overall fuel consumption for DOHC engines can be attained by maximizing the power band and transmission/differential gearing. What this means is, since it has more power on tap, one can easily accelerate to a desired speed with less effort, so less fuel is consumed. But this is primarily dependent on driver skill already.

Also as mentioned earlier, DOHC engines typically have more valves per head, than its corresponding SOHC variant. With that, the DOHC takes full advantage of valve train control to attain optimum power or fuel economy, again this is dependent on the design of the engine.

There are inline engines that have either SOHC or DOHC. On the other hand, there are non-inline engines (either V shaped or boxer engines) that can have either as well. Some V6 engines, for example, have one camshaft per side so the right bank of three cylinders has one camshaft, while the other side has another one. There can also be two camshafts per side, so that effectively makes it four camshafts in total.