Myth : Tetrahedra (4-sided elements with 3 corner nodes per side) should be avoided as they are not as accurate as Hexahedra (6-sided elements with 4-nodes per side, also known as bricks). Similarly 4-sided elements are better than triangles.
Related myth : Automatic meshing which produces mainly tetrahedra is not to be trusted. Far better to build up groups of brick elements slowly by specifying 4-sided regions in an input file.
Reality : This is only true for simplex elements (those with only corner nodes) but is emphatically not true for quadratic elements (with additional midside nodes). Again it seems to stem from academic teachings where the teacher only ever taught or used simplex elements. However, I cannot repeat too much, do not ever use simplex elements for stresses in the real world!
Confirmatory comparison tests on real-world objects, using the same element types as Femdesigner, are in this paper.
There is one advantage to be gained from using Hexahedra; often the output plot looks prettier for shapes which are themselves brick-like when the mesh is coarse. However, if the mesh is coarse then it should be made less so.
Note that simplex elements are often called first-order and quadratic elements are called second order. This refers to the order of the polynomial where first order means to the power 1, ie a line, and 2nd order denotes a parabola to the power 2.
One reason why simplex elements were traditionally preferred was because for Abaqus, Ansys, and several other big-name FE products, contact elements didn't work well (or at all) with higher-order elements. This was never true with Femdesigner and is no longer true elsewhere due to the use of better algorithms but perhaps many people didn't get that memo.