See, if you look at the page for Koloomn / Ultimate Block Party, it lists the Japanese version as just Kollon, the same name as the arcade version. However, there's also an entry for a later version called Korokoro Kollon, so you'd assume it's an upgraded version not released in the West, right? You're close! Korokoro Kollon is an upgraded version, as it adds wifi play and several extra modes including the Tutorial, Puzzle Challenge, Training Solo and Campaign... Basically, the modes in Koloomn / Ultimate Block Party. It's supposed to be the other way around- . The PSP game just called Kollon is a (mostly) straight port of the arcade game, only adding in Vs. CPU mode and the characters that appear in it. So, in case you were worried, you're not missing anything by going for the Western releases. Although I'd go for Koloomn just because the title screen's better.
What makes this more confusing is that, as told to us by reader avery, it would appear DHM- a different publisher from the European version's publisher, 505 Game Street- planned to release another version of the game in Europe on PSP (and DS, we'll get to that), entitled Korokoro Cubix, in 2008... Two years after Koloomn was released in Europe! Most of the info that exists on Korokoro Cubix pertains to the DS version, but a press release shown in this YouTube video specifically mentions plans for a PSP version. It does show that there were a few additions planned for this version, specifically two extra characters, one of which- a giant robot- you can see in screenshots of the DS game on JeuxActu (which is where the boxart above comes from), but it's unclear if these were going to be exclusive to the DS version or on the PSP version too. In any case, both versions were cancelled, so we'll never know. Speaking of that DS version...
Taisen!! Kato-chan no Kororonpe!- 対戦!! 加トちゃんのころろんぺ! in Japanese- is essentially a reskinned version of the game... And what a reskinning. The Kato-chan of the title is Cha Katō, a Japanese comedian best known in video game circles for being the Kato-chan, the star of Hudson Soft's true magnum opus Kato-chan & Ken-chan, released in the US as J.J. & Jeff. He's still at it, and in particular this game uses a cartoon charicature of him which I can't find an exact origin for, but can trace as far back as 2000 as the basis for a series of tourist tchotchkes called Otochi Katochan, or Your Local Katochan (here's an example of what they look like and here's a map of them that doesn't work anymore). More recently, you can find this charicature as a set of LINE stickers with noises so if you really needed to hear a tiny Kato-chan fart every time you send a message to a friend, you are in luck.
So, Taisen!! Kato-chan no Kororonpe! is a pretty straight port of the PSP version of Koloomn, with obvious changes made to the interface to make it work on the DS screens- your pit is on the bottom screen, with your character (or your opponent) cheering from the sidelines on the top screen. There's no touch screen controls from the looks of it though, as you do everything with the D-Pad and buttons. While it maintains the comic book / manga-style panel look for backdrops and the like, all the characters have been replaced with different versions of Kato-chan, including a robot and a police officer, presumably based on the regional versions of Otochi Katochan, and there are now nine of them in total who you fight across Japan in the new story mode. The big addition here is a challenge mode similar to Nazo Puyo mode from Puyo Puyo games, giving you a set of problems to solve with a limited number of moves at your disposal. There's also some kind of achievements system where you earn trophies based on in-game actions, a section for letting different Kato-chans dance and move, but that's about all I could figure out about this release. I think I prefer the PSP version mostly because the blocks are even smaller in this version which can make picking out yellow, orange and red blocks even more difficult than before, but if you really want the game on DS with a few extras here and there, this is pretty solid. Inexplicable, but solid.
As mentioned earlier, DHM was planning on releasing this version internationally but with all the Kato-chan stuff removed and the Koloomn cast put back in under the new title Korokoro Cubix, which never happened. No real explanation behind that one, but if I were to guess, I'd wager they somehow didn't realise the game had already come out in English-speaking territories, and decided it wasn't worth bothering with? Other than that, I don't have a clue!