Short answer: If you measure IQs, taller people tend to show higher numbers, and men are taller in average. A man and a woman of the same size would show a slight difference in favour of the female. If measuring intelligence as brain components, men show slightly higher numbers and have a better short-term memory.
Adam Hampshire from the University of Western Ontario has very recently conducted a research with 100,000 participants of different age, gender and geographical locations, criticising the use of IQ tests as a measure of intelligence. They run cognitive tests that analysed the memory, reasoning, attention and planning abilities, and reinforced them with MRI scanning.
For a century or more many people have thought that we can distinguish
between people, or indeed populations, based on the idea of general
intelligence which is often talked about in terms of a single number:
IQ. We have shown here that’s just wrong. Results from the study found that given a broader range of cognitive
tasks, the differences in ability relate to at least three components
of intelligence – short-term memory, reasoning and verbal aptitude.
These three components combined create an intelligence, or "cognitive
In other words, there is no single measure of intelligence. The components interact with one another but are handled by three distinct nerve “circuits” in the brain.
I wanted to mention this because IQ has been used as a measuring tool since the 1900s. They were created by French psychologist Alfred Binet, but Binet himself did not believe that his psychometric instruments could be used to measure a single, permanent and inborn level of intelligence (Kamin, 1995).
Works like the one cited on this answer have actually been critisised by Satoshi Kanazawa and Diane J. Reyniers in 2009.
The orthodoxy in intelligence research for the second half of the 20th
century had been that men and women had the same average intelligence,
but men had greater variance in their distribution than women. Most
geniuses were men, and most imbeciles were men, they said, while most
women were in the normal range. This conclusion, however, was
manufactured out of political expediency. Not wanting to discover, or
a priori denying, any sex differences in intelligence,
psychometricians simply deleted from the standardized IQ tests any
item on which the performance of men and women differed.
Kanazawa and Reyniers ventured another hypothesis. They started with something that had been stated before: that height is positively correlated with 'intelligence' (sources), taller people on average are 'more intelligent' than shorter people. And men in every human population are taller than women. They analysed a large representative American sample (20.745 from the National Longitudinal Study of Adolescent Health) and discovered that:
Once height (measured in inches) is controlled, women have
significantly higher IQs than men. Net of height, women score 2.14
points higher on the PPVT. In contrast, each inch in height is worth
more than half an IQ point (0.56). Further controlling for health,
physical attractiveness, age, race, education, and earnings does not
alter this conclusion. Height has exactly the same effect on
intelligence for men and women: Each inch in height increases the IQ
by about .4 point.
Because American men on average are 5 inches taller than American women (5'10" vs. 5'5"), this translates into 2.80 IQ points (overcoming the 2.14-point advantage of women). According to this study, when height is not controlled, men show higher IQs in average.
These are still just abstractions for what we want to define as intelligence (
g, Hampshire's ratio). Kanazawa's work offers a plausible explanation to why IQ tests show higher numbers for men, but I think it's Hampshire's research that shows a more flexible approach to the subject. Intelligence has environmental modifiers:
Source: Fractionating Human Intelligence
Age was by far the most signiﬁcant predictor of performance, with the mean scores of individuals in their sixties 1.7 SD below those in their early twenties.
However, the games you play, if you are an anxious person or if you smoke, all modify your final
g number, or supposed intelligence.
And here comes what I think is a possible answer to this question:
While the differences between male and female participants’ mean (0.1
SD), verbal (0.03), and reasoning scores (0.03) were negligible, males
showed a small advantage over females on the STM component score (0.2
Are men smarter than women?
If you measure IQs, taller people tend to show higher numbers, and men are taller. According to this, taller men are (generally, very broadly) 'smarter' than shorter men and shorter women. In average, a man and a woman of the same size would show a slight difference in favour of the female.
If measuring intelligence as brain components, men show slightly higher numbers and have a better short-term memory.
This is the latest study using 'modern' technology such as MRI scanners. The brain is still the most complex structure we possess, so I doubt any of this will remain carved in stone.