When Mantic Games released its Kings of War rules there were complaints from some quarters about its use of the IGOUGO turn sequence. The phrase, an abbreviation of "I go, you go" refers to a game in which one player takes a turn moving, shooting and fighting with their miniatures and then the other player does the same. This is contrasted with something that might be called "alternating activation" in which one player chooses a miniature and does something with it, then the other player, then back to the first and so on until the turn is over.*
IGOUGO has been criticised for being unrealistic as it does not allow players to respond to their opponents actions and because the 'passive player' has to wait for long periods of time before being able to do anything. These long waiting periods can make IGOUGO seem dull or jerky in contrast to AA's fluidity or dynamism. There is even a tendency to regard IGOUGO as slightly old fashion or out of date, a complaint that was leveled at Kings of War and at each edition of Warhammer that continues to use it. When Privateer Press announced their new big battle supplement for War Machine, stating that it would use AA, many applauded it as a step forward. As though the move represented a progressive shift, instead of a simple rules choice.
Alternating activation often goes along with the abandonment the of traditional turn sequence. Specific movement, shooting and fighting phases are usually lost in favour of allowing units to move, shoot and fight when they are activated, before another model does the same. One notable exception was Rackham's Confrontation, which used AA in its movement phase, before having separate shooting and close combat phases afterwards.
AA is very common for skirmish games, possibly because the quick back and forth between players better mirrors a dual or brawl than the careful maneuvering the characterises a big battle. There are, however, some big battle games that use this approach. Games Workshop's Epic Armageddon is one example and soon War Machine will follow. However, one aspect of large scale battles that is not easily modeled by AA is co-ordinated attacks.
In a game that uses IGOUGO game, with the turn divided into stages, it is easy to have one unit or miniature attack another and then be joined by a supporting ally. The actual combat resolution doesn't happen until later allowing multiple units to join the attack. This is much more difficult to model in AA. If one unit or character activates at a time, with no separate phases, then one unit completes its attack before another can join. It is possible to have combat engagements last over several activations, but this requires the initial attacker to survive the first attack.
Imagine a situation in which two weak units attack a stronger one. In IGOUGO they can both engage and the combat is worked out in one go. In AA, the first unit has two attack and survive a potential counter attack before its ally joins it.
There are ways around this problem. Malifaux has a companion rule that allows some groups of models to activate together, for example. However, these are generally compromises or fudges that work around the natural flow of the rules and arguably undermine the fluidity of Alternating Activation.
The point is that AA feels more fluid and sometimes more real, because the way the miniatures or units activate feels closer to simultaneous. However, the fact that allies cannot easily act in concert undermines that by demonstrating that it is still turn-based. Wargaming is necessarily a fudge that does its best to simulate the effect of real warfare whilst allowing players to actually play a game. Ultimately, Alternating Activation is as much a compromise as IGOUGO, they just have different strengths. Alternating Activation simulates the back and forth of combat, IGOUGO is better for co-ordinating strategies and careful maneuvering.
*This is a slight simplification as many games that use some variation of AA have a mechanism that allows one player to activate two or more miniatures or units in sequence. Broadly we are talking about a system in which one player gets to activate some, but not all, of their models and then the other does.