I did a simple folded size comparison of the Brompton M6R with the Dahon MuEX. Not entirely a fair comparison, as the Dahon MuEX has 20 inch wheels which are larger than the Brompton's 16 inch. Still, this shows the size difference between the Brompton and the Dahon fold.
Top view, side by side
From the side by side view from above, it can be seen that the Dahon is longer than the Brompton. This difference is quite significant, as it is longer by at least 10cm. This difference is enough to determine whether you can put the bike sideways or straight into the back of a car. If you have space for two folded Dahon side by side, you can probably fit 3 Bromptons into that same space.
Top view, end to end
As for the width, both of them are actually quite similar. The Dahon MuEX is using non foldable pedals, which causes it to stick out more at the side. Ignoring the pedals, the Dahon is just slightly wider as the wheels are a little further apart. The chain and derailleurs are also exposed on the Dahon, which makes it more prone to damage.
Lastly, for the height comparison, the Dahon is just a little bit taller than the Brompton. This can be the difference that prevents the Dahon from being stored under the table or a shelf.
Overall, the Brompton is a little lower, a little narrower, and quite a lot shorter than the Dahon. This makes it ideal for compact storage, as it can fit under most tables or just into an unused corner.