In vanilla veterancy is a nice bonus, but nothing really more than that. It adds +1 to melee attack, defence & leadership per rank, and slightly improves reload speed. LO does not change this, but instead improves the effects of veterancy via the red line skills.


Red Line Skills

For each red line decision skill (See Improved skill trees) there are three choice available. This includes 2 choices for how to upgrade a unit(s) with the third choice being 'Treasure Hunt.' Treasure Hunts are randomly generated events that you can choose if you do not plan on taking the unit(s) in the current lord's army, or if you don't have the DLC to use them.

The other two choices offer 3 effects each to upgrade your forces.

The first effect will unlock immediately.
The second effect will unlock once the unit(s) reaches veterancy rank 4 (One Silver Chevron)
The third and final effect will unlock once the unit(s) reaches veterancy rank 7 (One Gold Chevron)

So in addition to the small bonuses provided by ranking up, you can also unlock powerful new effects for your forces, which can include stat buffs, contact effects, abilities and attributes. This is why veterancy is important in LO, and therefore unit preservation is much more important if you wish to get the most out of your forces.