It is great (and that goes for the pre-4.0 version)!  I wrote a review of it here.  I haven't had a chance to try 4.0 yet. 

Can't say I care for it.

   It's a very good game if you like strategy games.  It's basically a mixture of 4x strategy and tower defense.  With the new 4.0 update, all the graphics in the game have been redone and it has a new graphics engine.  I like supporting the company as well.  So far, they've put out a couple of expansions and they put out a lot of free dlc in between.  They new 4.0 update has 147 new ships included and they didn't even charge anything for it.  Good game, and the AI is extremely good.  There's lots of messages on their forum about how good the AI is.  Definitely encourage any interested in strategy gaming to try out the demo.

It's an enjoyable game if you like these things:

1) RTS (even though it's slower, still an RTS)
2) Playing against stacked odds - the AI always starts out with everything other than your home colonized/defended.
3) Playing against a purely reactive AI.

The third point bears explaining - the AI in AI War is 100% reactive. It has some scripted timed events (like every so often with a bit of variation, launch wave of ships of strength <how much you pissed the AI off> against player), but those are separate ships not part of the AI fleet. It only responds to your actions, it does not do anything by itself. As such, its behavior is also highly predictable. If you jump into a system and attack an AI command post, the AI will "free" the defenders from their positions around outposts/harvestable asteroids to come and attack you. If you destroy that command post, 100% of the time the AI's ships in that system will try to attack one of your planets, the only variation is which planet they'll go for. As such, your goal is to figure out how to destroy the 2 AI Core Command Stations (the one and only winning condition) without pissing off the AIs too much. Almost everything you do increases AI threat, which means they get bigger reinforcements and send tougher waves at you, and if you are not careful, the AI becomes literally unbeatable at high enough threat ratings.

There are many AI behaviors that give them bonuses/handicaps, and there are very, very many ship types which are randomized for both you and the AI. The randomness is what makes the game fun, along with the different AI abilities - some might focus on heavy defense, some might focus on heavy attacks, etc. There are lots of these, so even though the AI is reactive, there is good variety and different ways for dealing with each.

The demo is likely far outdated at this point, but should still be a good introduction to the game, that's how I got into it. I haven't tried the new 4.0 yet, though my total playtime of the game clocks in at around 86 hours.