Particle shape, Particle size, Particle size distribution
Not too far ago one can find a choice between spherical and irregular particle shape. Not any more. You probably still can buy columns packed with irregular particles, but there is no benefits even in terms of its price. There are definitely no benefits in terms of efficiency. Irregular particles could not be packed with the same efficiency as spherical. So, if you have a choice between spherical or irregular shape - choose spherical.
We already discuss the effect of the particle size on the efficiency. The smaller the particle size the higher should be the efficiency of the column, but remember that it is dependent on the column length.
Important is that there are always the distribution of the particle sizes. If you see that particular column packed with 5 m particles, this is just a median value for particle diameter. In fact there are some particles, which has 4 m or 6 m diameter. If particle size distribution is wide, than you may have 3 and 7 m or even 2 m, to the lesser extent certainly, but they are there. It does not give you any benefits it is only decrease column efficiency and increases its backpressure. The narrower the particles size distribution the better, the more uniform packing bead.