do planar or electrostatic speakers inherently

sound fuller at moderate volumes than cone speakers?
No, I have both. I do think they sound better though for other reasons at those volume levels.

In my experience, I tend to agree with your statement.

My ML Sequel IIs sounded better at moderate volumes, than they did at realistic sound levels. However, my Revel Studios sound better at realistic sound levels, than they do at moderate levels, albeit slightly.

(I think this had something to do with the speaker designs, and my not be inherent to all planer/electrostatics vs. dynamic speakers in general. The Sequel II was a little brittle at loud volumes, whereas the Studios really come to life when pushed.)

My two cents worth anyway.
I don't know about sounding "fuller", but...

Full-range electrostats tend to maintain the same tonal balance across a wide range of volume levels including very low levels, and usually have excellent detail and articulation so that you can still hear everything that's going on at low volume levels. In my opinion, full-range electrostatics are unsurpassed at low volume levels.

Planar magnetics tend to be not as good at maintaining tonal balance nor inner detail at very low volume levels.

Direct radiators may or may not do a good job with tonal balance at low volume levels; higher efficiency ones do best. Degree of detail also varies. When there's not enough, you have the urge to keep turning it up.

Note that these comments are generalizations.

I beg to differ.

I had the electrostatics (ML's Aerius, Aeon and Ascent), planar (Magnepan), single driver (Fostex in MLTL, still have it). At present, I have a 3 way active(Linkwitz Orion) speakers.

The Martin Logans sounds good at low level, but no bass. Maggies like to have power to wake it up. If you plan to listen at low level volume with maggies, IMO, you are asking too much! The single driver is also good at low level listening (mine powered by an 8 wpc SET)but dynamics is not for my taste. I prefer powering them with a modified Dynaco ST-70.

The Orion on the other hand have the full balance of tone, dynamics, and width of the soundstage at low, medium, or head banging levels. There is something different with an all active system. The balance of tonality and power distribution does not rely on how good the power amp handles the passive crossover because the amp only "sees" the driver impedance, nothing else. Yes, the Orion's active XO (ASP) plays a very big role in it. But since we are talking about low level listening, I would recommend for you to listen to the Orion from an owner near where you live and see for yourself. I bet, IMHO, that you have never heard anything like the presentation of this speakers has at low level volume, and beyond.

Of course, I not affiliated to the manufacturer! Etc. Etc.
I think this perception, if it's what you mean by "fuller", may have more to do with the radiation patterns of line-sources vs. point-sources, rather than with dynamic drivers vs. planar drivers per se -- provided the panel speakers we are talking about are tall enough to behave as in-room line-sources in the far-field.

I'm not sure I know exactly know why the characteristic radiation patterns and the ways they load the room tend to produce these psychoacoustic results (theory below), but it does seem to be the case that while typical point-source speakers (actually, usually multi-point-source or simulated-point-source) sound like the sonic presentation grows larger with increasing volume and shrinks with decreasing volume, true line-sources sound much more like they're simply getting louder or quieter with changes in volume, without the perceived "size" of the presentation (or if you like, distance of the listener from the performance) appearing as much affected.

I'm not sure if dipole radiation also plays a role in this, but my suspicion is that it's primarily an effect caused by the tall cylindrical wavefront. I'm also not sure if there's anything to do with the fact that most microphones act as point-source "listeners", but I believe that point-source speakers also diplay more of the correlated behavior where it seems there's just one "correct" playback volume setting for any given recording at which the program sounds most "realistic" through those speakers in that room, while planar line-sources (I don't have much experience with line-sources that aren't planar) don't seem as "picky" about this factor.

I'll be interested to see how many agree with this. My assumption is that since it's a well-recognized quality of line-sources that they don't appear to fall off in volume with increasing phyical distance (in-room) from the listener as rapidly as point-sources do, it makes sense that there must be a correlary relationship where if you change the volume setting rather than the distance, the "apparent distance" from the listener to the recorded performers will also not appear to change as rapidly, thus creating the impression of a more constant presentation size independent of loudness.
I cannot generalize to all speakers of these types but from my direct experience living for some time with examples of both types of speakers I can say absolutely YES to this question for the speakers I have owned.

I currently own both Merlin VSM/SE w/BAM and the full range Sound Lab Auras. The Merlin speakers deserve all the praise they receive and are truly wonderful speakers. As a caveat, I live in an apartment and admittedly my room is far from ideal. I also admit to probably never providing ideal (sufficient) power to the Sound Labs. However, I do a lot of listening at night and, therefore, at reduced volume, sometimes at very low volumes.

I am more than astonished at the Sound Lab’s ability to maintain tonal balance at incredibly low volume levels. To my ears, many, perhaps most, speakers seem to loose bass richness as the volume decreases. The Sound Labs do not. They remain completely balanced to almost inaudibility! This characteristic is growing on me. I like it a lot and it is part of the reason I am migrating from the Merlin to the Sound Lab for more and more of my listening.

If you, as I, have experienced a normal shift to “thinness” with decreasing volume for most speakers, then hearing the Sound Labs would be a revelation in this regard. You have to hear it to believe it and then to appreciate it in contrast to most other speakers.

Both of these speakers posess many other positive characteristics, I tried here to address the one in question.

Yessss! When I give a SoundLab demo, I like to show off just how good they sound way down at very low volume levels. I think the bass holds so much better than with other speakers at low volume level well because a woofer's suspension system is to a certain extent "sticky", and the stickiness is overwhelmed at normal listening levels but looms dominant at very low output levels. The ultrathin diaphragm of the SoundLabs (still to the best of my knowledge the thinnest in the industry) has no such "stickiness".

When I bought my first pair of SoundLabs, I had to sell just about everything else to afford them. I drove them with a three hundred fifty dollar solid state amp, and while the volume level was limited it was still the best sound I had yet heard in any audio system. I could listen way down at barely audible levels and still enjoy it immensely, and so far I haven't encountered any other speaker with that characteristic. Of course when I eventually got bigger amps they sounded better, but nothing was as huge of a leap as bringing in the SoundLabs that first time.

In case anyone doesn't know I'm a SoundLab dealer folks, so grains of salt all around.

From my experience, the answer is yes, when you are talking about typical dynamic speakers, but, horn systems and other high efficiency systems also sound very good at lower volumes.

Another low volume phenomenon that is a big advantage of dipoles is that sound is concentrated in the listening area between the speakers and is much more attenuated to the sides. This is because the front and back wave are out of phase and they cancel where they interact at the side of the speaker. So, at any given subjective volume level in the listening area, there is less annoying bleeding of sound to other areas of the house. I was surprised how substantial is this effect, when I switched from Martin Logan electrostatics to a horn-based system.
My Apogees sound pretty much the same anywhere in the room...they do not get louder when you walk up to them to any large degree.