Good, but not the best it could have been.
Graphics
They are amazing, and probably the best part of the game. I was completely convinced that no game could trump the visuals in God Of War 3. Santa Monica shut me up real good with Ascension. Kratos has some of the same kills (like the centaur finishing move) and when I went back to see it done on GoW3 the vast improvement blew my mind. Though I am now hesitant to say this is the pinnacle of what a game can look like on the PS3, seeing as this generation is coming to a close I will conclusively say that this will probably be as best as any game will look (unless, god willing, The Last Guardian ever sees the light of day and manages to outshine it).
Story
The storytelling was confusing. I know God of War games strive to give gamers a movie experience with huge widescreen epic "shots" that zoom out during a battle or when you're crossing a huge bridge, but the time leaps were a leap too far. If I remember correctly, the story jumps back three times to a few weeks before the opening scene, but I found that there wasn't enough back story to warrant a time leap. Once it jumped back to the present I felt lost because I had completely forgotten that the game had jumped back, and keep in mind I finished the game in one day. Each jump would take about 2 hours before leading back to the present time. I think it would have done better to simply use cutscenes as a way to tell story that was left out.
I also felt that the whole story was a weak attempt to explain why another game needed to exist. Chains of Olympus felt like it had a place in the story since it was the first prequel to the trilogy and it gives little explanations such as how the titan Atlas came to be doomed to carry the world on his shoulders and what became of Kratos' daughter Caliope. That last act of the game was pretty heart-wrenching. I'll even say Ghost of Sparta had its place in the saga. But Ascension seemed much more like a throwaway, its only saving grace being the inclusion of a multi-player mode which I didn't try out.
Gameplay
The gameplay was decent. I liked the inclusion of Hades' souls as a power you could summon since the Claws of Hades were a favorite for a lot of people in GoW3 as well as the lightning powers that came from Zeus' power-up. I do have to say that I missed be able to switch completely to a new weapon such as the Nemean Cesus. The accessory weapons in this game felt like the equivalent of bombs when playing Zelda. Once they were used up, you would lose them and that was pretty disappointing. Otherwise the battle mechanics felt very familiar to me.
All in all, if a fun action-packed game with some platforming and puzzles is what you're into, then that's what you'll get. But if you're looking to find out more about Kratos' story, you'll be more than a bit disappointed.