Planars/ Electrostats benefits over box speakers?

I'd agree with Marty that the most distinguishing characteristics is 1) the geometry of the reverberant field and 2) differences in how air is pressurized ie you mostly just hear the music whereas with good dynamic drivers you probably can also feel it when called for.

Having owned both Maggies (1.5's and MMG's) and Martin- Logans (Aerius) I feel compelled to chime in. Without getting too technical about how they produce sound let me say that their biggest advantage over box speakers is simply NO BOX. They both produce such a natural uncolored sound that when heard for the first time it can be very unsettling to many an audiophile (me included). So much so that some people will simply say "I gotta have these". However, if hard driving power Rock is your thing then please look elsewhere. But for softer Jazz or Steely Dan and such I can't think of anything I'd rather listen to them through than a set of Maggies. I currently run Ohm's simply because they handle anything and everything nicely but if I ever have a third music room I will definitley have some 1.7's for those late night Jazz listening sessions, anyway just my 2 cents...

I also like Marty's post. Another advantage is there are no cabinet colorations caused by resonance and reflections.

Small panels have less bass and often employ a dynamic driver that is difficult to integrate in to the sound of the panel. Although I think Sanders does a good job at it, the best I have heard are the large electrostatic speakers. Those have phase advantages; i'm not sure if cone drivers can be as good in that area. To get first hand knowledge of panel speakers listen to more brands than Magenpan and ML.

Having owned Maggies and as well big boxes, well...

Generally the planar speakers give full sized images (and boxes miniaturized versions --- even most big boxes) and, as pointed out earlier, you look up at the stage rather than down. In these regards the planar speakers are much, much more realistic sounding. But...

they must be played loud (at or near live acoustic volumes) to have the palpable presence and body to work well. I have never heard a planar speaker do ambient music (background-level volume) very well. they must be driven and have a great deal of amplifier current to do so.

Finally, the Maggies for me had to go for a non-sonic reason (or, an indirect sonic reason). To sound right, they need to be 4-4.5 feet into a room. Not many places accommodate a pair of 3ft by 6 ft panels out 4 to 5 feet into a room. So, unless you have a dedicated listening room that is spacious, room set-up is difficult. Fitting a planer-based system into a regular living area (with other purposes for that room) is not easy and most spouses won't connect with that at all.

Polarin mentioned OHMs, which I prefer these days over planars as well. OHMs and Walsh style drivers in general are a totally different breed of "box" speaker for many reasons. I replaced my Maggies with OHMs most recently. I hear Magies still on occasion at dealers and gotta say there is nothing I miss about them still. If I did not listen to pop/rock/electronic music as well as all the rest, I might feel differently. Can't speak for other planars, but same true for Electrostats I have heard like QUAD. I wanted the QUAD sound but with all the large scale dynamics as well that I found limited. OHMs pretty much do it all for very reasonable cost that will vary directly with room size only.