UPDATE: The Pioneer is installed.
Okay, I've been listening to the MB Quart for about 10 months, so I feel I'm quite qualified to give a solid opinion on which sounds better in our cars. I've been really pleased with the MB Quart. You can read over this thread to see how happy I've been with it. It was a solid choice, and I was bummed when it died.
Well... not any more. The Pioneer blows it out of the water. It's honestly a bit shocking how much deeper and harder the Pioneer hits. Aside from being a little larger, it also weighs about twice as much, so that probably has a bit to do with it. I'm now bummed that I didn't get the Pioneer to begin with. It's so much better. Also, it's not just high volume where it's better. It has more presence at moderate listening levels as well. I'm very happy.
Technical details: My settings are identical. I didn't touch a thing. I did have to open up the hole in the box with a jig saw to fit it in the smaller MB Quart hole. It only took about 5 minutes and was quite easy. That's it.