Which sex has higher variance of reproductive rate in modern societies - male or females?
Sperm are cheaper than eggs 

According to Bateman's Principle the males of a species are (typically) more able to produce a greater variance in the number of offspring. This is because generally the males can produce many gametes and achieve many matings whereas females are limited by the number of eggs, resources, and time lost to pregnancy. Therefore, just by simple logic, it would appear likely that males have greater variance in mating success (strong/attractive males would be able to mate with many females while weak/unattractive males would have little to no offspring). See Wikipedia for an introduction to Bateman's Principle. Also see this paper about sexual selection and mating success variance.

An Example

An extreme example of higher variance in male mating success is that seen in lekking species. These species form groups of males called leks where females enter and choose mates. Often one/few males will sire the majority of offspring in the next generation. Fallow deer are one lekking species where males have higher mating success variation than expected by chance.

In Humans

Here is a blog post discussing a paper which showed that males have greater reproductive success variance than females in humans. In the paper see table 1 (Vm:Vf column) which indicates the majority, particularly those close to ancestral type lifestyles, have much greater variance in male reproductive success. Only one measured (Finland) is the reverse pattern.