One can argue that Projective Geometry is more complex than Euclidian Geometry (it is less intuitive and came after), but some behaviours are easier in the projective world (two lines always meet).

One can argue that Projective Geometry is more complex than Euclidian Geometry (it is less intuitive and came after), but some behaviours are easier in the projective world (two lines always meet).

There are also lots of cases where results are proved for dimension high enough, but get harder in small dimension, like the Poincare conjecture.