It really depends from person to person. You can decide based on what you are more interested in. Big Data and Data Science are both data-driven but differ in their end applications. Big Data deals with massive chunks of data and Data Science, on the other hand, employs machine learning algorithms for creating statistical models and generates insights from the said ‘chunk of data’.
Big Data helps organizations to better gauge the market, boost efficiency, and add competitiveness. Data Science studies the potential of Big Data through modeling techniques.
If you are interested in the implementation of statistics and predictive analytics, you can pick Data Science. Professionals in this domain are good with scientific methods, programming tools, and models.
Big Data professionals are good at handling diverse data types from various sources as well as data processing. Big Data professionals are proficient in Hadoop, R, Java, Tableau, Hive, and creating reports and dashboards.
Here is a video to draw a clear comparison between Data Science and Big Data.