Above the modal dominated frequencies--300Hz and up

There are basically three types of loudspeakers as far as I'm concerned: ones whose off axis behavior bears little resemblance to on axis, loudspeakers with Wide radiation patterns and ones with narrow radiation patterns.  Most speakers are of the first type and of little use to me for building a listening room, home theater, or mixing/mastering studio since we hear the early reflections as part of the original(to a degree) and not all listeners will likely be in the sweetspot.It would be hard to treat your room to correct for wild sound radiation patterns unless you were to make your room anechoic. There's a belief that you can EQ poor loudspeaker radiation patterns, but you really cannot EQ acoustic problems.  This is an acoustics problem so every problem you "fix" will create another.  Newer software corrections seems to be improving these erratic loudspeaker's perceived behavior.   Let's assume we want to hear the recording and not get into the wild world of mini monitors and unruly loudspeaker radiation patterns and you don't have the latest experimental room correction software.

Ok, wide pattern loudspeakers:  above is a Linkwitz Pluto
(  http://www.linkwitzlab.com/Pluto/specs.htm  ) and we have a graph of one right here on the Blog--the Behringer 1030A:

So what sound effects can we expect from this type of speaker in stereo?
Spaciousness, good envelopment (sometimes described as 'liquid sound' or a 'wash of music' on audiophile sites), an improved vertical dispersion compared to narrow directivity, and detail.  The "detail" seems to be a result of the ear getting 'a second look' according to Dr. Floyd Toole's proposal.  The 1030A gave me so much detail, I heard things in recordings that really shouldn't be there and thought the speaker must be broken.  I was wrong as I was later able to hear the same low level flaws on other speakers, just not to the same degree as they were exposed through the wide radiation 1030A.   Some potential negatives from this system of loudspeakers has to do with early reflections that can be loud enough to cause image shift or poor imaging.  I've never heard this as a 'real' problem, but I know others who claim it is.  Source broadening is real and a vague image could be described.  Others might say it fills in spatial gaps...  So is this a problem?  That's up to you and the goal you have in mind. The only time I've ever heard a serious image problem from reflection was with a Martin Logan panel speaker.  Some sounds seemed to be coming from the front wall and the soundscape was essentially a mess.  Imaging was out of the question.  The guy next to me thought this effect was very cool.  Panel speakers fall into my 'not to be discussed' category.  These broad output patterned speakers tend to be small, inefficient, and require a lot of power for high output that they can't comfortably handle.  They also tend to have a wide vertical window which makes them excellent near field monitors and a less abrupt change from omni radiation to wide in the bass to midrange transition compared to narrow pattern speakers.  In theory this could give them an edge in tonal rendition.  The Linkwitz link has a ton of info on setting these speakers up.
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Then narrow directivity made famous by Dr. Geddes and a version of his Summa The graph is displayed above and used to be posted here:
http://www.gedlee.com/summa_.htm
It was removed for more advanced displays and/or perhaps an upgraded design.  I'll post this one for comparison sake and it's similar to my early attempt at loudspeaker design shown below.

Dr. Geddes advocates this type of system for many, pardon the pun, sound reasons--too many for me to go through them all.  Essentially you can crossfire speakers with a tight toe in.  The listening axis would then be off the center of the speaker by around 20 degrees.  This is said and confirmed by my experience to have excellent spaciousness because of the high level of contralateral reflections, good interaural cross correlation, and precise imaging for many listeners.  It reduces the influence of the room and very early reflections which are perceptually significant (these designs do not help most SBIR issues) and ITDG but suffers in near field performance due to large variations in FR with small movements and the narrow vertical and horizontal patterns--refer vertical polar response written earlier in the blog.  THX recommends this type of speaker as does recent work of Princeton: http://www.princeton.edu/3D3A/Directivity.html though for use in a different way.  The problem I had with type of speaker was caused by my particular design.  You can see the ragged treble response and this resulted in some treble harshness.  Graphically Dr. Geddes's speaker doesn't seem to posses this issue.  It's just a better design well executed.  Other things of note is that these speakers--narrow directivity--generally use a powerful, large diameter pro woofer and a waveguided compression tweeter.  These tend to make a big, dynamic, and easy sound that pretty much any amp can drive them to THX reference levels and beyond.  One particular advantage for the Summa is the fact that it maintains its pattern nearly to the region where a room goes modal and essentially becomes part of the source!

The other 2 speakers graphed in detail on this site are somewhere in between as far as directivity is concerned: the Behringer B2031P and the Mackie HR 624 mk2 with the Mackie leaning more toward the narrow.  The B2031P displays some of the off axis nastiness that my design had but less pronounced.  Reverberant rooms will expose this off axis nastiness more than than dead ones and reducing the very early reflections with these speakers is definitely a positive as is adding cotton balls in the ports beside the tweeter.

That's pretty much the basics of above the modal region and it should give you much of the info you need to make a reasoned decision about sound quality and buying a loudspeaker.  I'm sure I will edit and update this in a few days or so.  How much output and power handling will need to be addressed as well, but there is plenty on the web about that and little about this.

Next we go below 300Hz to Mars.
Study on optimum loudspeaker pattern for imaging.
How loudspeaker pattern effects perceived tonality.
Genelec Paper on Diffraction
Some Rationale
More Rationale