Pure maths is maths done for its own sake, while applied maths is maths with a practical use. Applied maths tries to model, predict and explain things in the real world: for example, one area of applied mathematics is fluid mechanics, which analyses how fluids are affected by forces. Other examples of applied maths might be statistics or probability theory. Pure maths, on the other hand, is separate from the physical world. It solves problems, finds facts and answers questions that don’t depend on the world around us, but on the rules of mathematics itself. This is roughly what a pure mathematics student is required to study before research.
Analysis , Abstract Algebra ( groups , rings , fields , ... ) , Topology and differential geometry , Theory of numbers .
This is roughly what an applied mathematics student is required to study before research.
Analysis , differential equations , linear programming , Abstract algebra ( not in that much detail ) , numerical analysis , dynamics and some other things. Generally speaking, applied mathematics might be viewed as easier by those who would struggle with the way more abstract pure approach. It might be the better choice if you choose your subject, not because you are interested in it, but because you hope to optimize your job hunting.
But what is best? If you would like to study pure mathematics, obviously pure mathematics would be best for you. If your interests lie more within the applied area, you should go for that.