Planars/ Electrostats benefits over box speakers?

Sunnyjim, I have been a long time ( 20+ yr) owner and advocate of Magnepans. I picked up a used pair of Coincident Triumph Extreme II monitors and they outperformed my MG 3.7Rs in nearly every respect. Coherence, accuracy of timbre, and resolution were all clearly superior. The coincidents matched the Maggies with respect to tight, fast, articulate mid bass. I found the low frequency roll off started higher, but was a more gentle slope with the coincidents, so that there was actually more useful information below 40 Hz with the coincidents. The only aspect where the magpies were superior was in the range covered by the maggie ribbons.
The Coincidents with stands are substantially less expensive than the 3.7Rs. I highly recommend that you consider the Coincident TE IIs, especially if you are interested in a small footprint.

It's all about recreating the reverberant field. To do it effectively the speaker needs to produce full range sound (woofers in addition to tweeters) through the reverberant section and at a level approaching that of the front primary driver level.

A big benefit of panels for me is one that isn't talked about enough: Full size images! A grand piano is HUGE, and a good recording of one sounds that way through panels. Through most boxes they sound miniaturized. Panels also create a soundstage you are looking up at, rather than down on. The best deal in panels is the Eminent Technology LFT-8b. They aren't that big, 1' wide by 5' tall, and match better with tube amps than do Maggies, being an 8 ohm load rather than 4.

It's hard for me to generalize on which type of speaker (planar vs dynamic) produces better timbre, because there's a ton of variation on that front within both types. Some people believe that planars are "faster" and offer more detail, but I wouldn't generalize and would again argue that there's a ton of variation IME in the perceived "detail" delivered by stats vs planar magnetics vs ribbons, and (to a lesser extent) among different designs within each type of planar.

If you're looking for an advantage that's generic to planars, I'd agree that it's mostly related to the dispersion characteristics. The reverberant field usually sounds richer and more natural to me, possibly because there's less variation in horizontal dispersion vs frequency in most planars vs most dynamic speakers. Imaging also differs qualitatively, as does sound staging. However, personal preference is likely to determine which presentation you prefer on those fronts.

I also feel that dynamic designs have some common advantages (bass impact, for one), so it's back to trade-offs.

Have fun with the search.

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.