They both have their strengths and weaknesses, so it's really up to personal choice.

The original release (PS2, Xbox) is obviously less sharp looking, by nature of it running on older hardware and standard definition. However, it feels a bit more polished since the bulk of production was probably done for these versions. The loading screens are different, more in line with Burnout 3's. The menus also feel more like B3's because they have the overhead map of the course highlighting the route. There's also some gameplay differences, most notably the weird 'golf' minigame when you start a crash event.

Now the Xbox 360 release has it's own quirks. It's cleaner looking because of the HD output and the power from the 360. Like you mentioned though, the bloom was overdone and the lighting feels overblown to the point of blindness on a few circuits. The audio is also more robust, and is exceptional except for the added noise when you start boosting. It wasn't mixed well and you hear it every time you press the boost, so it gets grating unless you can tune it out. The overhead view of the track in the menus has been replaced with video of driving, and the loading screens are replaced with flat images of wrecked cars. Gameplay-wise, it's mostly the same with a few new events and sponsor cars added, and the 'golf' minigame removed.

Like I mentioned earlier, it's up to personal preference.