In general,
God of War: Chains of Olympus controls incredibly well. Most of the more glaring issues are because of hardware deficiencies, but Ready at Dawn has done a great job at working around them. Most of the controls remain the same and the only time you'll really notice differences is when you have to use the shoulder buttons. The setup works well when using certain moves or skills, but feels odd when trying to evade since you have to press both buttons down and move the analog nub. Though it feels odd at first, you'll eventually get used to it.
As in past games, the Chains of Chaos are Kratos's primary weapon and can be upgraded by spending red orbs. Eventually Kratos will also earn the Gauntlet of Zeus, which is essentially a giant fist. Kratos can also learn new magic attacks, such as the efreet, which causes fire damage to nearby foes and a shield that allows Kratos to throw back some attacks like a discus. Magic attacks are useful, mostly for taking down bigger enemies.
Quick-time events play a slightly bigger role in Chains of Olympus than previous games. Nearly every enemy you come across features some sort of minor event. On one hand, it helps give the game it's unique feel, though Chains of Olympus goes a little overboard with a few of the events. There's also a slightly greater risk when attempting some, especially when it comes to Cyclopes or shield-bearing phantoms, who will quickly use your failure to inflict a lot of damage.
God of War: Chains of Olympus is a faithful recreation of the console versions of the game. While this is a really good thing, it is also a bad one since it doesn't bring anything new to the table. While a few more puzzles or a new mechanic would have been nice, Chains of Olympus is still a great addition to the PSP library and worth playing if you are in the market for a new action game.