DOHC was introduced to improve the volumetric efficiency of a given engine, lending itself to more power. DOHC breath better and result in higher power and RPM as oppose to SOHC. If DOHC doesnt make power gain directly but they are used in higher power config cars. DOHC is expensive to produce that's why these days most normal car runs on SOHC or OHV to cut cost. All big performance cars majorly run on DOHC engines. SOHC engines are MUCH cheaper and easier to maintain, but they don't have quite the performance or fuel-efficiency that the DOHC does. DOHC layout is better than a SOHC layout in many ways, in DOHCs, the valve timing is more precise, and better valve lift is achieved. also, a DOHC setup eliminates the need for rocker arms, hence creating better timing, and valve contact is more direct too. So a DOHC is "better", but SOHC is cheaper.
http://wardsauto.com/technology/gdi-dominates-ward-s-10-best-engines-list
3.0L TFSI Supercharged DOHC V-6 (Audi A6)
2.0L N20 Turbocharged DOHC I-4 (BMW Z4/528i)
3.0L N55 Turbocharged DOHC I-6 (BMW 335i coupe)
3.6L Pentastar DOHC V-6 (Chrysler 300S/Jeep Wrangler)
2.0L EcoBoost DOHC I-4 (Ford Edge)
5.0L DOHC V-8 (Ford Mustang Boss 302)
2.0L Turbocharged DOHC I-4 (Buick Regal GS)
1.6L DOHC I-4 (Hyundai Accent/Kia Soul)
2.0L Skyactiv DOHC I-4 (Mazda3)
3.5L DOHC V-6 HEV (Infiniti M35h)