Ok, I start.
The problem occurs in Inpedendence Day Five Star Collection DVD. I have Pioneer 565A DVD player. I don't have a surround so I use always stereo mixdown in all DVD's. Now, with Dolby 5.1 channel mixdowned to stereo in my Pioneer, some explosion effects sound a lot quieter than Dolby 2.0 track. The sounds when those buildings explode in chapter 26 or when the first missile hits finally the ship in chapter 52. Those effects rock the walls with Dolby 2.0 track but in Dolby 5.1 mixdown they sound not so impressive. But, now is the strange thing coming. I used to have a Panasonic DVD-A560, it's a 1999 or 2000 model DVD player. In that one, both Dolby 5.1 and Dolby 2.0 sound the same in Independence Day. Those sound effects rock the walls also in Dolby 5.1 mixdowned to stereo. So, the players differ in mixdown I thought. But I was wrong.
I figured out that those effects come mostly from the center channel, so I disabled mixdown. I connected the center to one of my speakers and checked only the center channel. I did it with both my DVD players. In Pioneer, those sound effects from the center sound again quieter than Panasonic. So it's not a problem of mixdown. It's something else. I don't know which sound is the one the producers intended. Either the Pioneer's center output is quiet or Panasonic's center output is louder. But the most strange thing is that this happens only in Independence Day. I checked lots of other movies and the Dolby 5.1 > stereo doesn't differ from Dolby 2.0 in case of sound effect volumes. The quality varies (which I cannot hear) but the volumes of different sounds are the same in both settings. So, in Independence Day, there is something strange going on.
Do you have that DVD? Can you try it with downmixing 5.1 to stereo and check if it differs than Dolby 2.0 track in those chapters with those effects? Also without downmixing.

Btw, I checked the movie in my computer and there, both 2.0 and 5.1 tracks sound the same. This time they are both quiet in case of those sound effects. Which is also strange.