Why does unstructured grid approach is more accurate than structured grid approach? I appreciate your opinions?

In fact I feel that the other way around is the correct. The structured grid approach should be more accurate if it utilize the same grid quality in the high gradient solution zones. The reason for that is the interpolation schemes utilized are more consistant and the intergration along the faces in FV formulation should be of second order or close to second order if the grid is not uniform. Where as the order of the discretization is hard to keep in second order in the unstructured meshes.

also.. consider the memory requirement for unstructured grid compared with structured grid for a large and complicated geometry.

J-

Even if your discussions of order were correct, that would not make sense. The order of accuracy refers to an asymptotic process of grid refinement, such that the grid distribution function remains unchanged. For any given grid, any method (e.g. first order) can be more or less accurate than another discretization method (e.g. third order). Since in practice one can rarely reach the level of refinement when asymptotic relations hold, this is in fact the most common occurence, when 1st order method can be more accurate than higher order discretizations especially for rapidly varying problems. For a simple of model of that, check out the curve fitting with different polynomials.