Who has a more varied reproduction rate in modern western societies - men or women? The average rate is the same of course, but I wonder which sex have higher variance - higher variance means that reproduction is more concentrated in some subgroup of given sex so this subgroup transfer their genes at higher rates then averaage rate in whole population. The next question would be 'is that subgroup somehow homogeneous' ?
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 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.
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.
The problem with Bateman is that he was only looking at zygote production. There are many more factors influencing reproductive variance aside from number of sperm vs. number of eggs. If I were you, I'd read the book titled "Dr. Tatiana's Sex Advice to All Creation: The Definitive Guide to the Evolutionary Biology of Sex." The author is Olivia Judson (by the way, it's a very fun read and it is hysterical :)). In her book, she gives numerous examples of species wherein the females have a much higher rate of reproductive variance than traditionally thought. I hope I've helped!