Yes, tis true!  Cushions are generally the same way. It's just part of the cut. These shapes carry more weight in the bottom/belly of the stone than other cuts do.

Obviously, every diamond is different and the depths will vary, but generally, the belly of those cuts needs to be deeper to achieve the cutting.

Therefore, they generally have a smaller millimeter outline for thier carat weight than one would expect.

As an example, a 2.00ct round is about 8mm across. Where an 8mm asscher would be closer to 3.00 carats.

Yes, it's true for the most part. My asscher is .91 carats and it's about the diameter of a 3/4 carat RB. I've experienced a tad bit of what I think people refer to as "shrinkage" but overall, I love the cut so much more than a RB that it makes up for it. Also, they're just not seen around here and I like having something different. I've not met a single person with an asscher (in person), nor has anyone I've talked to even known what they are. They see square and think "princess" so I have to set them straight! 

I hate to generalize - because there are both Asschers and Cushions cut to 60% depth- even less- with great results.

These stones will appear pretty large for the weight.
For example: This 2.04

ITEM #: R1544
Emerald Cut Diamond, Loose

  WEIGHT: 2.04ct
  SHAPE: Emerald Cut
  COLOR: E
  CLARITY: IF
  MEASUREMENTS: 8.15 x 7.47 x 3.92 mm
  TOTAL DEPTH: 52.5%
  TABLE SIZE: 67%
  POLISH: G
  SYMMETRY: G
  FLUORESCENCE: NONE
  GIA REPORT #: 14351749

Price: $27500

Not technically an Asscher, it certainly looks quite like one to me.
A branded diamond will never be the depth of this one.
The 2.04 looks larger than a 2 carat round


ITEM #: R1757
Cushion Cut Diamond, Loose

  WEIGHT: 4.00ct
  SHAPE: Cushion Cut
  COLOR: F
  CLARITY: SI2
  MEASUREMENTS: 9.59 x 9.47 x 5.41 mm
  TOTAL DEPTH: 57.1%
  TABLE SIZE: 69%
  POLISH: G
  SYMMETRY: G
  FLUORESCENCE: NONE
  GIA REPORT #: 15664247

This cushion looks positively huge for it's weight.

A square takes up a lot of space, too. Lots of time in mms we'll have a round and it looks smaller than an asscher that is 8mm because the square just takes up more space. Hard to explain.

I don't profess to be an expert, just a lover of asschers, but in the long time that I searched for my stone, most of what I saw (which was not a lot) had small tables and medium to a lot of depth.  My vintage asscher has a very small table, a very high crown and is very deep (a lot of wasted diamond, cutting it back then I think).  I'm guess my stone looks a lot smaller than it really is, but I love it.

Just wanted to add that much of my reasoning on this stems from when I was looking for an asscher last summer for my new e-ring. I was told repeatedly by various vendors that asschers would face up smaller than other shapes and that it was not possible to get a well cut asscher in the millimeter size for ct range I wanted.

I was told that if I wanted an asscher that was cut to retain more millimeter size, then it would not be cut correctly and would not be as nice as it was "supposed" to look.

Just telling what I was told by various "professionals" at the time. So...... I opted for a beautiful emerald cut instead - which I DO love.. but if I had known that it is possible to get asscher cuts that "look big for thier weight", I would have probably gone that route.

I agree that I would hold out for one with a little lower depth.  That 2.04 is a dream!  Also, that 1.58 L has a nice size.  Hmmm. . . I think I hear that lovey calling its agent for a movie gig!!