Greg Nuckols has written a series of articles on this subject (with plenty of references).
In the first part, Sex Differences in Training and Metabolism, they show that it turns out that almost all differences in strength and performance are down to muscle mass (which "is attributable to males’ higher testosterone levels"):
In terms of muscle mass differences, females tend to have about 2/3 the muscle mass males do, with a larger difference in upper body muscle mass (about 1/2) than lower body muscle mass (about 3/4). And although males tend to be stronger than females, that difference is explained almost entirely (97%) by muscle mass differences. That means if a male and female have the same size muscles, they should have roughly the same strength.
So, just to get this out of the way early, the VAST majority of the differences between males and females that are relevant to performance aren’t necessarily sex differences, but rather can be primarily explained by differences in body composition. A female and a male with similar training and similar amounts of muscle and fat will perform similarly.
(First link is broken, probably should go to: Age and gender comparisons of muscle strength in 654 women and men aged 20–93 yr)
Apart from muscle mass, there's also a difference in the distribution of muscle fibers, where women have more Type 1 fibers (which are more enduring) and men have more Type 2 fibers (which are more explosive).
In Strength Training for Women, the Key Points are kind of telling:
While men start with more muscle mass and strength, relative strength gains actually tend to be larger in women, at least in the short term. This is especially true for younger women and upper body strength gains.
Long-term, relative rates of muscle growth and strength gains are probably roughly equal for men and women, though women may make slightly larger gains, relative to their starting point, across their entire training career.
Women are not just "little men." While relative muscle and strength gains may be similar, there are key differences between men and women that impact training and recovery.
Some elaboration on point 3:
For starters, women tend to be less acutely fatigable than men, meaning they can generally do more reps per set at a given percentage of 1RM, do more sets with a fixed number of reps at a given percentage of 1RM, or both. There are several factors underpinning this difference, but the two most important seem to be a) women tend to have a higher proportion of type I muscle fibers, which are more fatigue-resistant and b) women tend to have less muscle mass, so they don’t occlude blood vessels quite as quickly when lifting, meaning they can more efficiently deliver oxygen and clear metabolic waste products from their muscles. (However, I’ll note that this isn’t a unanimous finding).
Second, women may recover from training a bit faster than men (one, two, three). [...]
Third, men and women may respond differently to low-load training. At this point, there’s a tremendous amount of evidence showing that low-load training (i.e. sets of 20+ reps) can build muscle just as effectively as heavier training (though just because you can build muscle effectively with low-load training, that doesn’t mean you should). However, only one of the studies comparing high-load and low-load training was done with women. It found that women training with higher loads (6-10RM loads) gained way more muscle than women training with lower loads (20-30RM loads). This stands in stark contrast to similar studies performed on men, suggesting that women may respond to normal, heavy-ish training the same way men do (mostly doing sets of 5-15 reps), but may not respond as well to low-load training.
So, to answer the question as stated:
Do women gain strength slower with the same intensity of exercise? Let's say there would be two people with identical physique (height, weight, initial strength, age) but of different gender. They both start weight lifting (for example) and they work out with the same intensity and duration and eat the same food. Would they end up equally strong?
In general, yes, they would wind up more or less equally strong. The exact results would depend on the design of the training program. Women (generally) benefit from higher volume than men, whereas men (generally) can gain more muscle at lower intensity.
However, the "assume identical physique" part isn't really realistic, since different physiques are part of the difference between the sexes. If you compare men and women with similar total muscle volume, the men will almost always have stronger upper bodies than the women, and the women will almost always have stronger lower bodies than the men. Also, for a woman to have the same amount of muscle as a man, she will likely have trained more and so be closer to her genetic maximum (while the man's muscle mass will be the result of less training and more testosterone).
So a better question would be "are there any differences between the sexes in how much they can increase strength and muscle mass, in relation to where they started?" The answer is "no, no major differences". Might even be that women can increase slightly more, but men will still be stronger since they start out with more muscle mass.
I'm quite certain that, at least in the Western cultural context I live in, gender roles and other cultural factors causes a not-insignificant part of the relative strength difference between men and women (especially among untrained individuals, but very little so among top-level strength athletes), but this would be very hard to prove scientifically; and anyone who said it explains everything has a lot of evidence to provide.
As an aside, if we look at running instead, men are faster on shorter distances, but the longer the race, the narrower the gap, and at races >195 miles women appear to be faster than men.