Trying to figure out artillery is tough one to do. HPS/Tiller never really put much in writing about how it works. Other than when I fire artillery at enemy guns I always miss. When someone fires at me they hit. Even if I am entrenched. I am getting a little paranoid about this.
I have a better "feel" for how things work in Phased play. Also, it is easier to isolate cause and effect in Phased play. Turn play tried to merge movement and combat, and in my opinion very poorly, resulting in some odd behavior of the game. Apparently, fatigue is one of those things that didn't survive the translation in tact.
Originally fatigue was a result of casualties. A random modifier was applied to the actual casualties the Unit took to calculate the fatigue. For Fire combat it was 1 to 3 times the casualties. For melee combat the loser used a higher factor than the winner. For artillery a completely different method was used and I am not sure what it is. I know it has undergone changes because the artillery defense factor is now in the parameter table.
But the big difference between Phased and Turn play is fatigue recovery. In Phased play it takes place at the beginning of the Turn and only applies to Units that have not expended movement point, flagged as doing some action like breastworks or bridges, or having been fired on during the previous turn. Apparently Turn play lost this check or doesn't properly track it during the previous turn.