Well, when considering the plight of the common man, one must not ignore the elephant in the room: the aristocrats are fighting each other in bloody great robots that devastate the land and leave hundreds of bystanders dead in the wake of their battles, even worse when the conventional forces so insignificant we don't even see them in the scale of the battles are foolishly deployed against them by groups too poor to field even a single ATAC. And that's not even considering that these things are constantly shedding magical waste that leaves entire regions filled with all sorts of freaky stuff like blue tomatos and eldritch colours the human eye cannot fathom.
So, the major concern of the common serf at this point isn't so much that one or the other side win, but instead that the fighting be over as quickly as possible. No amount of oppression from an evil empire or freedom from tyranny under a noble kingdom from their perspective can justify even a moment's continued fighting from their perspective, because every second an ATAC is on the field more of their land is permanently spoiled, more of their babes will come out deformed, flesheating monsters, and more of their family members will be crushed by the uncaring metal titans who are their overlords.
Consider also that the proliferation of mass-produced ATACs adds a further danger to the common peasant, that posed by their work to those unlucky enough to be conscripted in the suicide gangs that piece together the grim machines. Sure, the engineers and designers are likely wearing enough protective equipment to survive exposure to the again powerfully magical components of the ATACs but the vast number of laborers required to build it? They're lucky if their families are even told where the mass grave they're buried in is (not that they could visit it, since the contamination of the land would ensure they had to join their family member there). Those less lucky are mutated into twisted freaks, forming an additional underclass who are literally untouchable due to the toxicity of their flesh.
If this weren't enough hardship, the fact that ATACs are viewed as almost religious icons by the local churches forces the peasantry even more harm, as they must tithe a substantial amount of their produce to be burnt as an offering to the Metal Gods. Those who defy this rule are subject to burning as heretics, naturally.
I suppose it's best now to actually talk about how the Kingdom and Empire are actually different in a day to day sense. The interesting thing is that for the average member of the lower class the Empire actually provides a much higher standard of living. Most of its land is unspoiled (at least until the disastrous Vanguard Wars, which we're seeing here) and its princess' attention to quality of life issues at home is actually the main source of the poor oversight of the military that led to the conflict. Meanwhile, most of the Kingdom is a backwards, blasted heath upon which humans can only barely scratch out subsistence living divided among almost monstrously corrupt feudal lords who exploit them to the bone (indeed one is rumored to have actually attempted to construct ATACs out of the bones of his serfs after their deaths, though it proved unworkable).
Of course since history is written by the winners, it is the popular perception that the Kingdom were somehow inherently more noble and just than the Empire.