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A major distinction between these languages is in their approach towards data science. R is used for statistical analysis while Python offers a general approach. Data science is a central part of the job for several growing numbers of people.
Python is a great option for analyzing and modeling data. With packages like NumPy and pandas, there are so many options to explore. In comparison, R still seems like a better choice, since the language was made with the sole purpose of data analysis. This can play a vital role in machine learning.
In the context of biomedical data science, learn Python first, then learn enough R to be able to get your analysis done, unless the lab that you're in is R-dependent, in which case learn R and fill in the gaps with enough Python for easier scripting purposes. If you learn both, you can R code into Python using rpy.