I recommend the following two articles that go a ways towards answering your question.
One: Sex Matters during Adolescence: Testosterone-Related Cortical Thickness Maturation Differs between Boys and Girls by Bramen, Hranilovich, et.al. Relevant quotes:
"Studies have shown sex differences in hormone-related brain maturation when boys and girls are age-matched, however, because girls mature 1–2 years earlier than boys, these sex differences could be confounded by pubertal maturation."
"The age-related developmental trajectories of male and female adolescents are different, and modified by androgen-receptor genetic subtypes, confirming results from recent studies of sex-differences in hormone/puberty-correlated maturation."
"Because frontal lobes are important for impulse control and risk/reward assessments, are known to functionally mature during puberty, and have important functional connections with medial temporal lobe structures, such as the amygdala, we expected to extend our findings to this report where we focus on cortical thickness."
A lot of literature for review here, but the gist is that girls reach sexual maturity earlier, which corresponds to the development of certain brain structures.
Two: Sexual dimorphism of brain developmental trajectories during
childhood and adolescence by Lenroot, Gogtay, et. al. Relevant:
"Both cortical and subcortical gray matter trajectories follow an inverted U shaped path with peak sizes 1 to 2 years earlier in females."
In summary and in (partial) answer to your question, with many caveats outlined in the above to papers, girl brains develop faster than boy brains. This may correspond to earlier "maturation" in the colloquial sense, if that sense is understood, for example, as the development of the frontal lobe, which is responsible for impulse control.
The issue of whether such differences are affected by nurture is not addressed in these studies. There is however strong evidence for significant physiological differences in the rate of brain development.