Quad element is more accurate than
triangular element.
Tria element is stiffer than quad,
which results in lesser stress and displacement if used in critical locations.
Consider any standard problem of plate
vibration for which analytical answer of natural frequency is known. Create two FE
models based on only tria elements and only quad elements (same element length). Tria
mesh will show higher value of natural frequency and will deviate more from the
exact answer.