Sorry for the wall of text, but I had to get this into a single thought.
I thought about two occurences during WW1 when I read this.
The first story goes that the Americans were shelling a little too close to a German hospital, so the germans sent over a runner and they brought an American officer behind german lines and showed him. When he got back he told them whats up and they quit shelling that area.
the second story is the famous christmas when both sides called a ceasefire and went and hung out together in No Mans Land for a day.
Both of these occurences show how similar the soldiers are, how much their wants are exactly the same. Think about it, your average Joe blow was probably drafted into the war, and all he really wants is to go back to his wife and kids, or his girlfriend, or even to go to college or something normal, something that everyone wants. The trick wouldnt be in characterization, the trick would be in making the two opposing sides seem eerily similar to each other.
my thoughts on the execution of this game would be something like this: the setting would have to be during another world war. A war where entire countries get drawn up into the fight out of mere bureaccracy. Something similar to WW1 where there were petty alliances between countries, then a small rebellion took place and the whole thing just escalates out of hand very rapidly and the countries involved didn't really have a stake in the fight to begin with, but they have their alliances to various countries and the whole domino effect of declaring war happens just like it did back in early 1900s. (seriously, go look it up. WW1 started in with turks and some other nobody country and wound up involving major world powers).
The people involved are two spec ops groups, one on either side of the conflict.
the first group you play as, the "winning" side, was created solely to destroy the spec ops group on the opposite side, because the opposite spec ops group was doing so badass and was doing too much damage. throughout the story, you hunt them down through various major battles, ambush them once or twice to seriously screw them up, then the final act is your last confrontation with them, culminating in the second in command being the final man standing and your character looking him square in the eyes before executing him.
the second group you play as is the one that you just spent an entire act hunting down and killing. It starts with their formation, and takes them through the battles that got them their status as a badass spec ops unit (the same status that got them a group specifically assigned to them) and then follows them as they get ambushed and have their numbers dwindle, see their commanding officer get killed, deal with all the crazy crap that happens to them in the "winning" campaign, but from a "losing" angle, all the way up to the final scene where your character (the second in command) having a barrel put to his forehead and gunned down.
both acts would focus on the normalcy of the people involved, how both sides weren't brainless, marcus phoenix meatheads or demonic hellrazers like what they thought of each other, they were fathers and wives and brothers and sisters and daughters and sons that were simply assigned a job. They would have to make both main characters relateable, so you find yourself agreeing with their ideologies and what they do and say, because they are so freaking normal (and not making one side demonic like what they did in battlefront, where the recorded catchphrases include "destroy the rebel scum." not exactlty relateable material) despite that they are opposing each other the whole time, so that you are torn between which side was "good" and which was "evil."
and I'm pretty sure the whole "kill the main character" thing would work, since they did it in CoD4.