It's not always this obvious but I picked this section to highlight the filter because it increases and decreases in strength on a continuous cycle.
Look carefully at the video itself, not the details and just keep your eyes focused, there's a cycle of increases static and graininess present on the 360 version. It's trying to make it look as if you're watching an old movie on a projector.
The colors are softer and more washed out because of this. If you stick an image through a filter such as this, you miss some very fine details. The way your brain works is that it fills in missing detail. Hence, for example when you see a high def movie you'll notice more imperfections in computer generated graphics. When you play a high def game on a low def TV it won't look better but you'll think it looks more real in a sense compared to real people you see on a low def TV, as opposed to high def people versus high def video game characters. The more you can see, the more your eyes take over and your brain stops filling in.
This filter works on the same principle, it softens edges, softens colors, so your brain does more work trying to figure out what it should look like and is going to fill it in it will in essence appear more real.
This is a very slight effect, you have to be paying attention to notice it. It's not a very big deal but it's the difference people are seeing in the two versions. Which is to say... they're almost identical. Some people are going to like the way the 360 version looks better, the people who aren't noticing the filter, and realizing what's going on.
Then again, most people won't notice that Madden 08 is going to have 60 frames per second on the 360 version. You won't see the effect, you'll just like the way one looks better than another and not be able to describe why.