The reason why Einstein's definition of gravity is considered more accurate than Newton's is because it takes account of more factors. Newton lived over two hundred years before Einstein and did not have the advantage of all the later scientific discovery and work that Einstein did.
Newton's theory of gravity did not allow for the fourth dimension, time. It had already been undermined by Maxwell's discovery of electro-magnetism. The effect light has on the theoretical equations Newton used to describe his theory of gravity had not been included. Einstein's theory of relativity involved a definition of gravity that took into account the curvature of the earth, amongst other things.
Newton’s concept of gravity is good for explaining the basic motions around us and still holds in many situations but the problem is that Newton made a mistake. Newton treated gravity as a force, and in working, gravity isn’t a force which accelerates. Scientifically speaking, gravity doesn’t exist like Newton defines it. Newton was never able to explain how gravity works and refused to even try.
Einstein concluded that gravity is something you ‘feel’ when you have a surface. Once that surface is removed, there is no gravity and you are weightless. All objects in the universe are simply free falling towards the deep hollow of the universe between space and time, and external barriers and forces like velocity, magnetic fields etc keep them from doing so. Gravity is simply a curvature of spacetime. For example, we are falling into the center of the earth because of its mass and we would keep doing it but the surface of the earth prevents us from doing so. The surface acts as a barrier and causes a curvature in spacetime. This curvature is the gravity we feel.
Newtonian gravity holds in 3 dimensions but fails when the 4th dimension of time is added. Newton’s theory treats time as a constant whereas Einstein defines gravity in a 4d space defining time as another dimension. Einstein’s definition holds true both experimentally and theoretically and is therefore considered more accurate.