EU is separated into two portions of gameplay: strategic and tactical. In the strategic layer, you build your base, search for missions to fight aliens, perform research, etc. The tactical portion is the meat of the game where you take turns moving your troops around the map, and battle aliens using a wide variety of weapons including guns, grenades, and rockets.
One of the things that EU does extremely well is the risk reward system that permeates both the strategic and tactical portion. Often times, players are required to make tough choices, whether it's moving out of cover into a vulnerable position to flank an enemy or saving one city over another against an alien attack. Every action can have a domino effect over the next and makes the player aware that there is no easy path to win the game. The game even has an Ironman Mode that prevents the player from saving the game and loading it later to escape bad consequences.
EU is a much more streamlined version of the first XCOM game. For example, the concept of ammo has been removed and the maximum number of soldiers that can be brought in a battle has been reduced from 20 to 6. This allows for faster action and more emphasis on tactics over soldier micromanagement.
Players can develop their own approach to the battlefield with the introduction of classes and skill trees for soldiers. For example, players can use heavy soldiers to destroy cover and take out groups of enemies, use the support class to heal and provide smoke cover for teammates, or use the sniper class to annihilate single enemies with pinpoint accuracy. The skill trees further specialize a soldier because the player can only choose one of two skills when a soldier levels up. For example, in the support class, one of the choices is to pick between the enemy suppression fire skill or the skill that allows teammates to be revived.
My big complaint about this game that prevent it from being a 10.0 are the bugs that occasionally occur. What is really frustrating at times is running into bugs that further reduce the player's control without any reasoning. Some bugs include enemies teleporting out of nowhere (sometimes in the middle of the player's squad), shots not counting as flanking shots even though the enemy is clearly exposed to a soldier's line of sight, and enemies not being affected by grenades. One of these bugs occurring could be the difference between winning and losing a mission. Having these types of bugs in a game where every action counts is simply unacceptable.
Another complaint, albeit much less significant that the previous one, is the lack of story driven events. The game does a good job of explaining the story and providing cutscenes in the beginning of the game. This becomes much more scarce during the middle to near-end portion of the game. This may seem like a small complaint, but having a story driven mission or cutscene sprinkled in now and then would improve the flow of the game, add some drama, and break up the repetition of fighting one battle after another.
Even though I ranted a little bit, I still think EU is the best game of the series. EU brings the best elements out of the original and streamlines them to please old fans and welcome casual strategy gamers in.