This is advice to a prospective student wondering whether to go into public health/epi or biostatistics. I'm willing to blindly argue for biostatistics, but prospective students might find it more useful if I frame the issues so they can decide for themselves. 

Biostatistician or subject matter specialist? Do you want to work in one discipline or do you like to move around? Not sure what exact field you want to work in?

From the perspective of scientists, biostatisticians are natural generalists. Biostatistics is great for people who like science, or better, for people who like sciences. As a kid, when asked what I wanted to be when I grew up, I had a long list of 'ists' that I wanted to be. As a biostatistician, I can work with an environmental health scientist this morning, then work on maternal and child health in South African townships in the afternoon. I teach classes to apprentice statisticians. These apprentice statisticians work with scientists from a variety of fields on a wonderfully varied set of research questions and data analyses. In some classes, I teach scientists: political scientists and epidemiologists, educators and emergency room docs, health policy wonks and psychologists, geneticists and nutritionists and the occasional urban planner. And after they've taken my class, we can talk and communicate at a higher level than we could before they took my class. And we've written papers together, because they still don't know enough statistics to solve their data analysis problems but now they can handle the software and understand the issues if we talk things through together.

The world needs both specialists and generalists. In the discipline of biostatistics, biostatisticians do specialize. I specialize in Bayesian statistics, hierarchical modeling and longitudinal data. Other people specialize in psychiatric statistics or causal inference or survival analysis. 

Scientists ask biostatisticians how to analyze data, and, to analyze their specific data. They ask us how to design studies, and, to design their specific study. We write data analysis plans, we do power calculations, we analyze data, we report results. We teach statistics, and we figure out better ways to analyze data.

Statistics or biostatistics? Biostatistics is not much different from statistics. In biostat, we're usually concentrating on analyzing data from public health, medicine, biology and public policy. Statisticians can do that as well. 

Did you want to go to med school? But you preferred math? Biostat may be for you!

How do we analyze the data? How should we analyze the data? What can we do in the time available and with the budget allotted and with the skills we currently have? What's the answer? How do we even get to an answer? What does the answer mean? How good is this answer? Those are the questions biostatisticians discuss and work on and ponder and figure out how to answer. We do this in the context of particular data sets, working closely with scientists and advocates and doctors and teachers to help them understand the truth of their data and the truth of the world seen through their data. Biostatisticians do this generically, at a higher level, thinking about how to analyze data sets like this data set. We develop statistical methods that will help analyze classes of data sets, not just a single data set. 

Public health trains scientists, advocates and educators. Epidemiologists or community health scientists or anthropologists or environmental health specialists are usually scientists, and some are advocates and some are educators and some are combinations of all three. Health policy produces managers and also scientists. Biostatisticians are scientists, but we are general scientists. We know how to do science and we know how to think about science. We have a general outline of science sitting in our heads; when we learn about a particular study or discipline, we fill in that outline with more details, but the outline never goes away. In grant writing: we know the endgame: we know what we will do with the data we're proposing to collect. The endgame tells us whether the experimental design will return the information the scientist needs and it points us to better designs to collect data. We know where we're going so we can advise on how to get there.  

In academia especially, ​biostatisticians get to do all the fun stuff: designing studies, analyzing data, talking to students and other statisticians and scientific colleagues about what it all means, writing up results. We leave the difficult annoying time-consuming mind-numbing stuff to our colleagues​: figuring out what questions to ask our subjects and how to phrase them, actually collecting the data, keeping the mice and feeding them, storing the data, though we dive in and consult as needed. 

What do you want to be when you grow up? I want to be an environmental scientist, a paleontologist, a nutritionist, and an epidemiologist. I want to talk to physicists and computer scientists, biologists and geneticists, engineers and business people, field workers and economists. I want to be a biostatistician.