Which of the five main branches of chemistry has the most labwork?
All the five so-called branches of chemistry require heavy use of the brain. Modern chemistry is very interdisciplinary. At the research level, the distinction among these branches becomes blurry. Everyone is doing some part of each branch. Traditional inorganic and organic chemistry both require a lot of wet work and synthesis and characterization.
If you ask which branch of chemistry has the highest level of automation, and most of the work is done by instruments-it is analytical chemistry. Many modern physical chemists or theoretical chemists rely on in silico techniques (=computers, modelling, simulations etc). You may not be doing a single real experiment (if your not lucky). Computer is your virtual lab. As a hardcore theoretical chemist, finding a job afterwards in the field, may be difficult. My acquaintance switched to computer programming after a PhD, which was a wise decision after remaining jobless for a year. He learned programming languages in the mean time. In any case, all fields are good. It all depends on your passion.