OHV, or cam in block, or pushrod is a tried and true method. Its drawbacks are additional weight in the valvetrain which can limit its RPM potential, but its dead-nuts reliable with a short chain that rarely fails.
OHC or DOHC does simplify the valvetrain and make it lighter, but it relies on a long belt or chain that if it fails can cause a complete engine failure with damage to nearly all internal parts. The timing belt idea keeps rotating weight down, but its not very reliable and needs to be changed regularly. The chain is more reliable, but adds a good bit of friction and weight to the rotating assembly.
In most street applications, its rarely an issue. There are pushrod engines that easily rev to 10,000 rpm, and there are tons of DOHC engines that never go above 4000 rpm.
Its a design application, but in almost all cases, both can be designed to work in whatever application you want except the extremes. If you're designing a 16,000 rpm sport bike engine, you'd use OHC. If you're using a V-configured engine in a reliability application, it might be wiser to use pushrods for simplicity and keeping the car out of the warranty repair bay.