Empires: Dawn of the Modern World has 2 different game variants, action mode and Empire Builder mode, and a deathmatch version can be played with both versions.
Action mode in Empires is the more popular of the two kinds, and is about a 30 minute game. It involves a faster pace, and is more oriented at quickly building up a civilization and fighting with it. It is pretty well balanced, and some changes different between it and Empire builder. Some buildings and age progressions have different prices, and more citizens can harvest at each resource site.
Empire Builder is more of a slow paced game. It last a couple of hours long, and is many times over several ages. The age progressions take longer to reach, and resource gathering is slower. This causes much more of the focus to be on building a stable empire, and creating one that is built to last. Although skirmishes and battles still take place, everything moves slightly slower than action mode. Empire builder allows fewer citizens per resource spot, and buildings price and sturdiness is affected in Empire Builder.
Although not technically a game variant, deathmatch adds an important difference to the multiplayer game experience. Deathmatch lets every player start with more resources, and forces people to build an army quickly. It also lessens the need to have resource gathering, and much of the game revolves around building a civilization and an army before the other player (since you both start with plenty of resources).