Actually... the only real difference is in the number of camshafts.

A SOHC engine can also have 4 valves per cylinder, like a DOHC engine. The Honda Jazz and City only have SOHC motors. Yet despite both 1.3 and 1.5 liter variants being SOHC, the 1.5 liter version has 4 valves per cylinder, while the 1.3 liter only has three (because the secondary spark plug take up the space where the fourth valve would be).

Typically, it's easier to design a 4-valve per cylinder engine using two camshafts, and a 5-valve per cylinder (such as on the Toyota 20-valve 4AGE "Blacktop" motor) probably requires DOHC to work... but SOHC engines can be built in this configuration, also.

It's possible that you can be more flexible in variable valve timing with a DOHC head, and it's possible that DOHC heads may have more power potential, but Honda's SOHC R-engines (Honda Civic 1.8 and Honda CR-V 2.0) just blow that theory out of the water. Those two engines are at the top of their classes in terms of specific power output and fuel economy, and have one of the most advanced variable valve systems on the market today. They're much better day-to-day engines than the old K-series engines they're replacing, with comparable torque and horsepower with much better economy.

Of course, it's doubtful whether Honda can make an R-series engine as powerful as the Civic Type-R K20 (220 hp), as the R-series is an undersquare design not fit for the extra high revs that the K20 can develop, but in the real world, at least as far as Honda non-Type-R products are concerned, SOHC or DOHC is a moot point. Honda's SOHC engines can kick anyone else's DOHC blocks anyday...