Let me preface by saying that I've never actually played the original Katamari Damacy. After I finished the game I talked with other Katamari fans who played through the PS2 versions and then gave my PSP version a try. So I can answer a few questions right off the bat.
For those of you who don't know what a Katamari is, it's a sticky ball. You roll it around to pick up things and gain mass. In this game you need to roll up enough to make islands for homeless animals.
In addition to making your Katamari sufficiently large, some animals have preferences for Katamaris that have certain attributes, like sweet or hard, so you need to focus on rolling up appropriate items. You also have a limited amount of time.
For those of you who have played Katamari on the PS2, you do have to cope with the fact that you don't have two analog sticks. In fact, you control the Katamari with the digital buttons. There are a lot of different combinations to move it around, but the training level prepares you well. I found that I learned the basics, exercised them on easy levels, then went back to training to refresh on the advance moves. Within a few hours I was rolling like a pro. Whether or not you've played before on another system, you'll get the hang of it.
The sound is pretty much the same as the PS2 game, with a large variety of goofy Japanese pop songs and funny effects when you pick up various items. While this might not be the most graphically sophisticated game, it is arguably better than the chunky graphics from the PS2 version. You do periodically see 3D rendering mistakes, like missing panes, things moving through walls, and bad camera angles, but not enough to be really annoying.
What is annoying is the lack of variety. It doesn't take very long for the areas to start repeating, maybe with slight variations, but by about 2/3 of the way through the game most of the challenge was gone. Which is really too bad because this game isn't that long in the first place. I finished inside of 3 weeks, and I'm pretty slow. I rarely finish games, and I rarely play for more than a half hour or so at a time.
Somewhat better news is that Namco has given us a reason to pick up the game after we've officially won. There's a mini game you can unlock (actually two minigames), plus you can unlock Eternal Rolling for each of the islands, which lets you roll without time limits. This in turn lets you go back and collect things that you missed while playing through the game the first time.
Why would you want to do that? I dunno, exploration, maybe collection. Like a lot of Japanese games, collecting as much stuff as possible is a sub-goal. You can visit the things you've collected and see where the holes are. With Eternal Roll you have a chance to find the things you missed, which you might never have been able to get with a time limit.
In addition to the things in the environment that you pick up, you can also find "presents" of wearable items to change your character, as well as "cousins", which represent other playable characters. The cousins look different and have back stories, but as far as I can tell they all play the same.
There are a number of other points of interest, including the goofy "King" that is running the game. Sometimes he's really funny, but by the end of the game, even when he's spouting material you've never heard, the style starts to get annoying and you find yourself skipping the exposition.
Also you can take photos for your album, which you can also export to memory stick (or probably network as well). I didn't really mess with this, didn't much care. I didn't try network play, since I don't have anyone available to play with.
All in all I like this game and can recommend it, primarily because it is very different and enjoyable. Just beware that it's short. After finishing I went and unlocked Eternal Roll for about 2/3 of the islands, and collected maybe 80% of what there is to be collected. While I try to finish the rest? I dunno, so little time, so many games.