Actually both roles are recommended for someone from coding background. It depends more on the specific characteristics of each role in a company.
Data engineering is more about infrastructure work, which means parsing data files, storing data in particular databases (SQL or NoSQL e.g. Mongo-DB), designing databases or designing the pipeline of the data process.
Data Science is more about building models, selecting appropriate variables, performing exploration or validation of statistical models, hypothesis testing etc.. All these need good knowledge of at least one scripting programming language like Python, Matlab and R. In some cases there is also a need of Software Engineer skills for the implementation of applications related to Predictive Analytics or Machine Learning(or Statistical Learning).