I think it is difficult to precisely answer this question, as the way a child learns something is not necessarily the same as an adult does. Also, depending on the task, young children may be at disadvantage, due to their lack of abstraction abilities. A child may be able learn a language faster, but an adult may pick up subtilities such as humour, double senses etc. better.
Anyway, aside from these purely personal considerations, there seems to be quite a lot of literature at this regard: I am not a great expert on the topic, so I will just cite some papers but there may be more appropriate ones around.
For instance, face learning ability and time perception are better in adults than in children.
Where cognitive development and aging meet: face learning ability peaks after age 30.
Cognitive abilities explaining age-related changes in time perception of short and long durations.
Young children are also slower in learning new syntactic constructs compared to older kids or adults (in this case the abstracting capabilities of the subjects were tested)
Young children fail to fully generalize a novel argument structure construction when exposed to the same input as older learners
On the other hand, it has been shown that children can learn pronunciation of a second language faster and better than adults.
A one-year longitudinal study of English and Japanese vowel production by Japanese adults and children in an English-speaking setting.
The production of english vowels by fluent early and late Italian-English bilinguals.
it seems that learning music at a young age can influence brain structure in adulthood (but this is probably a slightly different problem from what you are asking)
Motor cortex and hand motor skills: structural compliance in the human brain.
On the same topic, this is an interesting read
Are there critical periods for musical development?
Citing from there:
Music is a complex human activity, involving many aspects and layers of complexity. Thus, there can be no simple answer to the question of critical periods for musical development. In general, more evidence for critical periods has been found to date for basic aspects of musical behavior, such as tonotopic map formation and absolute pitch perception, in comparison to more complex aspects such as scale structure, harmony, musical interpretation, and composition. Although in most children sensitivity to relative pitch and sensory consonance emerges very early in infancy, scale knowledge during the first years of life, and harmonic knowledge between about 6 and 12 years of age, the effects of early enrichment or early deprivation on the emergence of sensitivity to these various aspects of music pitch structure
remain largely unknown.We still do not knowthe answers to basic questions such as whether a person who is not exposed to music based on Western scale structure until the age of 2 years, 6 years, or older will develop the brain circuits for processing Western scales or Western harmonic structure or whether exposure to another musical system prior to this will help or hinder acquisition of Western musical structure.