A combination of the best levels from previous games, new game play tweaks, a new story and improved graphics.
I had missed both Katamari Damacy (never released in my region) and Beautiful Katamari (don't have an Xbox 360), so there was enough new content to make the game worthwhile for me. If you've played all previous games, then the three new levels might not be enough for you.
Whether you are playing new or old levels, there are a few changes compared to previous games. The first is the "Prince Hop", allowing you to jump. This can be performed by shaking the controller or pressing R2. I found the shake motion to be fairly unresponsive, so settled in to using R2 for the motion. This can enable new ways to solve old levels, and is required to some of the new levels.
The second change is the addition of hearts. When these are rolled up, a vacuum effect is enabled where all objects close by that are small enough to be rolled up. Depending on the type of heart, the effect is either momentary or lasts for a few seconds.
In keeping with Katamari's theme, both of these abilities work better with a larger katamari: you can jump higher and vacuum up larger objects respectively.
These changes make it easier to build a large katamari faster, so the game compensates with shorter time limits and stricter scoring. The result being that a strategy that gave 100 points on a previous game probably won't yield the same high score.
After completing the main story line, a new "Katamari Drive" mode will be enabled, which lets you play the levels again with a significantly faster forward rolling speed and even shorter time limits to match. Depending on the level, you'll either love or hate it. If you are trying to roll up everything in sight, it's great. If your aim is precision, it can be a pain.
An additional two modes are also available for most levels, which should unlock as you play the game. "Eternal" mode is the same as previous games, and plays like "Katamari Forever" mode with no time limit. "Classic" mode removes the new game play features and restores the time limits and scoring from the previous games.
With the game play modes out of the way, one of the first things you'll notice when playing the game is the new art style which resembles a cell shaded pencil sketch. It takes a little getting used to, but fits right in and looks great in HD. As you play the game, you can unlock additional graphical styles including the classic style (unlocked by playing a classic mode level).
The one place where the graphical changes can be annoying is that some levels are initially played in greyscale with objects gaining colour as they are collected. In most cases this works out quite well, but there are a few levels where rolling up certain things can end the level early and the lack of colour can make it hard to distinguish them from good items which can lead to a few frustrating failures. Fortunately the effect disappears on replays of those levels which limits the frustration.
Another welcome feature is the lack of mid-level loading screens. Players of the PS2 and PSP games probably remember the game pausing and the King popping up midway through the level while a less detailed larger scale version was loaded in its place. Those transitions are virtually gone, except for the largest scales and then they've been reduced to the order of a second or less. Of course, with the good comes the bad, and you'll be asked to wait while the game updates network rankings, auto-saves the game and sometimes updates trophy information after completing each level. Why they couldn't do these things in the background like virtually every other game is lost on me.
In short, this is the best looking Katamari game to date and is worth the purchase if you've missed some of the previous games in the series or no longer have a means to play them. Just don't expect any revolutionary changes from what came before.