I'll start by granting that I'm presenting a sort of false dichotomy here, as every war monument presents aspects of glorification and memorialization (the Tropaeum Traiani, for example, listed the names of Roman soldiers who died in the conquest of Dacia and had the sort of more conventional chest thumping battle scenes). But it does seem that the tendency now is towards mourning the lost rather than celebrating victory over the enemy--which makes sense for wars with controversial reputations like Vietnam or WWI, but even "good wars" like WWII tend to be memorialized rather than glorified. How did attitudes change regarding what aspects of war were appropriate to emphasize?
A certain side question is with the focus of monumentalization. Trafalgar Square in London is certainly a monument to empire in general, but also clearly set up as glorifying Nelson in particular. I couldn't really imagine the focal war monument for, say, WWII being about an Eisenhower or a Montgomery.
I think commemoration is a natural topic for archaeologists. Monuments are, after all, one of the few things that people purposefully make in the hope that future generations will come into contact with them and appreciate a particular original meaning. I'd like to highlight two memorialization efforts that have particularly interested me.
The Ingvar runestones. These runestones commemorated a number of powerful Swedish chieftains, captains, and landowners who died around 1040 in a disastrous expedition to the Caspian Sea under the leadership of a man named Ingvar. Surviving families erected as least 26 commemorative stones for their deceased loved ones. Despite our preconceptions about vikings glorifying death in battle, most of these runestones are more matter-of-fact memorials:
Hróðleifr raised this stone in memory of his father Skarfr. He travelled with Ingvarr.
Bergviðr/Barkviðr and Helga, they raised this stone in memory of Ulfr, their son. He met his end with Ingvarr. May God help Ulfr's soul.
Gunnarr and Bjôrn and Þorgrímr raised this stone in memory of Þorsteinn, their brother, who was dead in the east with Ingvarr, and made this bridge.
The interesting thing to note about almost all of these stones, however, is that they almost all tell us something about inheritance: Hróðleifr could point to one stone as he claimed his deceased father's land; Bergviðr and Helga could point to another to justify their reclamation of their dead son's property; the brothers Gunnarr and Bjôrn and Þorgrímr claimed their deceased brother's property, as well as rights to the bridge he had built. In effect, these runestones were not at all about glorification but were instead memorializing relationships that living people had had with their relatives who pre-deceased them.
Ireland's Memorial Records. Ireland, like Germany, had a problem after WWI: although many people in Ireland had lost loved ones during the war, it was inappropriate to celebrate their sacrifice. The Irish troops had fallen under the British flag, but the Irish Revolution of 1919-1921 removed that flag from most of the island. So how could they recall their dead?
The onus for memorialization came from none other than Sir John French, who had commanded British troops in early WWI before being appointed lord governor of Ireland. He initiated the commemorative effort even as Irish guerrillas were working to strip him of his rule. The idea was to publish a series of eight volumes listing every person who had died in the Great War, either claiming Irish descent or serving in an Irish unit. The brilliant artist Harry Clarke (think Nightmare before Christmas) was hired to illustrate these volumes.
These Records are a strange mix of glorification and more modest memorialization. On the one hand, Sir John French was trying to glorify Ireland's previous relationship to the British Empire. On the other hand, Harry Clarke's illustrations deface these soldiers and they always show up only in silhouette, often framed by nightmare scenes of desolate battlefields. Grotesque caricatures of saints and personified virtues gaze solemnly but not entirely sympathetically upon them.
Only one soldier (bottom-left) shows up with a visible face, lounging jauntily against a trench wall beneath a sky full of spotlights. In the most recent study of the Records, this soldier has been identified as none other than Charlie Chaplin, who featured in the wartime favorite "Shoulder Arms". Harry Clarke was among many fervent fans of Chaplin, and perhaps he used this image to connect those who grieved with a very humanizing portrayal of the war.
So these Records represent a precarious balance between glorification and memorialization. For a British general, the Records were a way to glorify men who had sacrificed their lives under his command. But for an Irishman who had lived through the 1916 Easter Uprising in Dublin, the Records were about men who had been stripped of their humanity by a conflict that could better be understood as a satire upon glory and honor. I'm still baffled by the way that these pages manage to preserve two so completely opposed memories of WWI and communicate both in just a single glance.
Sorry if this is brief, but I could never do it justice. I have listened to many of the Yale open courses (cuz, you know, grad school just ain't enough schooling). The modern European history course has a guest lecturer from (I believe) the art history department and he discusses this exact phenomenon with respect to WWI. You could just listen to that lecture if you're interested. I believe he even mentioned tropaea.
My first thought went to the Lion of Chaeronea. After Philip II wiped out the Sacred Band of Thebes in the Battle of Chaeronea, the Thebans erected this statue of a lion to honor their dead. It definitely wasn't chest-thumping since they lost the battle, but was strictly a memorial. However this might not fit what you're looking for because I believe it was constructed over the burial mound of the Theban dead and so could be seen as a funeral monument.