Here is how I see it. The second installment (to what promises to be a yearly occurrence) of the Purge was a lot better than the first. But it isn't because The Purge: Anarchy is a significant film. It's because Writer/Director James DeMonaco is finally able to incorporate the underlying theme of class hierarchy that was completely misguided in its predecessor.
The big mistake with the first film was making it a trite home invasion thriller. With Anarchy, we explore the outside world during the 6th annual Purge, and it proves, without a doubt, to be ten times more thrilling and suspenseful. We see the nut cases in freaky masks (one with GOD written on it) wielding their weapons of choice. We see the upper class citizens holding each others hands reciting the "New Founding Fathers" motto that feels like some satanic cult. In our seats, we feel that we have to look around all at times, because there could be a killer ahead or behind us.
There are three revolving stories of people who are entering the night. One is Eva and Cali, a waitress and her daughter. There is Shane and Liz, a crumbling couple with no killer instincts at all. And then there is Leo, the sergeant, the "kick ass and take names" guy. Leo is out to revenge Purge. The others find themselves wandering the street. Leo winds up having to protect them. Will his generosity effect his main goal? Can Leo really save everyone? Frank Gillo makes for a very convincing and likable hero. While we watch and the story unfolds, we learn that The Purge, and its purgers, aren't so much anarchic as they are regulated.
With it's unique premise the Purge is always able to separate itself from the average horror/thriller film. Most importantly, Anarchy is a step up because it realizes its potential to be truly scary from the realism of its "legal murder" concept; rather than just bludgeoning people left and right. Unlike the first film, your instinctive fascination with such a nightmare concept will multiply here, not diminish or turn into a laughing stock.
I can recommend Purge Anarchy. Not only does it save what looked to be a profitable franchise, but it is a decent film too.