Pushrod engines still use some sort of cam drive system, generally gears and a chain. Given their short path, they tend to last a long time, but still need periodic replacement. My small block hot-rod engine had a gear drive for reliability and timing precision.
Pushrod engines cannot rev as high thanks to the rocker arm and pushrod design. Not that you can't build a high revving OHV engine, but it requires some serious bits.
The real advantage of DOHC designs are the ability to have independant intake and exhaust cams. With the cams acting directly on the rockers, the valve train is light and high revs need light valve trains to keep from floating the valves. The four or five valve per cylinder designs also allow a greater intake valve area which means higher flow and greater efficiency.
OHV designs tend to be of higher displacement and square or undersquare configurations. The higher displacement is required as they have less efficiency, but the lower revving design means a flatter torque curve.
OHV designs do not inherently make more torque. It's the nature of the compromise that the OHV engine forces makers into. You could build a low revving square/undersquare torquey V-8 with a DOHC valve train, al-la Corvette C5, but most European designers wanted to shrink displacements while keeping power, and this requires higher revs. It depends on cam profiles, piston speeds, and gearing to really define the character of the engine/driveline.
1998 C230 "Black Betty"