Would it be easier to learn a second language as a child, when you've had limited exposure to language in general, or as an adult, when you already have a strong basis in your first language? Are there any studies testing this? Please include scientific research in your answers.
There are pros and cons to learning a language in any age group.
From the Frankfurt International School:
In fact, studies have shown that adolescents and adults are in many ways better at learning a new language than children, except in the area of pronunciation.
From the Max Planck Institute for Psychoanalysts:
In order to answer when one should learn a second language, one should first determine what one wants to optimize: the end result or time devoted to learning... [a] language which is learned before the ages of 6-9 is typically learnt to a level where the speaker has no detectable accent and is very comfortable using it.... On the other hand, if a language is learnt later, speakers may have a slight accent in their pronunciation but may otherwise reach a very proficient native-like level.
tl;dr While children do pick up on speaking quickly, they may not understand the ins and outs of their L1, which is a key part of learning an L2. Teens/adolescents will understand their L1 more proficiently, but they will falter in the area of pronunciation.
I don't have references at hand, but according to what I remember from my university-level SLA course, adults initially progress more rapidly than children with learning a new language, but at some point children's progress becomes clearly faster. If we compare ultimate attainment of a language, the correlation is quite clear: the earlier the initial age of acquisition, the higher the ultimate attainment. So in short, if you are thinking about the long-term perspective, the earlier you begin the better.
For more discussion and references, you can look at Understanding Second Language Acquisition by Lourdes Ortega (2008).