Note it's generally not by kills, but by damage done. Mortars can end up killing only 1-2 models but be Veterancy 2-3 because they've AOEed everyone in a squad. Furthermore, tanks generally get considerably less experience for killing infantry as their requirements are set very high compared to infantry and they shoot as less expensive stuff. SturmsTigers need to hit things like vehicle for that massive spike in veterancy gain while now the Brummbar vets up very well with the recent changes.
Rapid veterancy gain though is a Brit thing in general. Their army vets up incredibly quickly for certain units such as their tanks when they get the tank commander, previously Tommies, and units like the Mortar pit who have lower requirements compared to their price. though not by that much.
Regular 240mp Mortar Requirements
480/960/1920
Mortar Pit Requirements
700/1400/2100
Mortar 120mm
960/1920/3840
keep in Mind that mortar pit is atleast 1.5 mortars in Terms of dmg Output