Well, I think that the clown has the potential for excellence in either setting. The difference lies not in the scale of the circus, but in the attention given to the clown. Within the 3-Ring circus, the clown is often relegated to the (very necessary and noble) task of lubrication. The clown must be big enough, gripping enough, and human enough to attract the attention of every person in the audience - away from wild animals, cages, rigging, set changes, waste-cleanup, & entrances and exits. For a human, or group, to attract (or distract) attention from things to much larger (in mass) than herself(himself), s/he must be a clown of the highest order. Often, when the transition is complete, the clown must exit. Similarly, if the transition lags, the clown remains. This lessens the potential for the clown to follow any memorable plot/character arc during transitions.

Many 3 ring circuses feature Clown entrees, but (in my assessment): New Circus (or 1 ring circuses in general) shows offer far more time and focus to the clown as a presenter of crucial information concerning the human experience. The Pickle Family Circus, New Pickle Circus, and Bindlestiff Family Circus - as you say, are great forums for clowning. It is not necessarily about them having great clowns in CONTRAST to other shows...(at least not exclusively) but is also a matter of focus.
As an analogy, I'll reference the patron saint of postmodern clowns, "Buster" Keaton. When he was a supporting player in the "Fatty" Arbuckle shorts, he was good, but could have passed out of history as a footnote - had he not moved into his own starring vehicles. In the 3-ring circus, there is often ONE starring clown. In a 3 ring circus context, "Fatty" would have most likely outgoofed Keaton for the top billing, simply based on the scale of his comedy. In a one ring circus, Keaton would be Boss.

In addition to trends of focus/stage time, a difference in style is due to the scale. The 3-ring circus birthed the grotesque pantomime with amplified features (now ubiquitous and nearly synonymous with clowns) as a function of necessity. The one ring circus gives a closer frame of view. When viewed from close, the true human reactions can be seen, rather than merely the grotesquely-exaggerated. This all-but eliminates the need for "standard" clown makeup. While there are many examples to the contrary, particularly amongst the canon of cartoon and comic characters, I would contend that the unadulterated human face is more relatable and memorable than the painted. The painted face has universality, but the plain face has relatability.

The One-Ring circus brings humanity to the reception of the clown (and other performers), as the cinematic close-up brings subtle expression to the face of Keaton, Chaplin, Joan of Arc(or any other master of subtlety).

As for Cirque and the role/caliber of clowns therein... That's a hard one to approach because there have certainly been some stellar clowns who have worked (and still work) with Cirque du Soleil. Cirque's highly-stylized, big-budget, mechanically repeatable production style does seem to hinder the hellfire-nature of some clowns, but also affords the opportunity of huge-visions being translated. I'm thinking specifically of the "Storm" piece by Yuri Medvedev in Alegria. www.youtube.com/watch
I can't imagine a piece that intricate and mechanically involved being maintained by many/any circus for very long, especially given the angle of clown being portrayed. In brief: he doesn't get a single laugh... Many producers would cut this piece. American circus-clown has almost exclusively relied on gags and slapstick to convey clown logic. The surreal beauty of "Storm," like so many clown pieces, highlights the simplicity of human desires, and is, in my opinion, a rather bleak piece. I feel richer for having seen it, and am very grateful to Cirque for presenting it. On the other end of the spectrum, I am also thrilled to have the Antic-clowning of John Gilkey in "Varekai." John Gilkey, like Jeff Raz(Razz) & Diane Wasnak (Pino), joined Cirque du Soleil after the Pickle Family Circus, so it wouldn't be fair to say that Pickle has great clowns, while Cirque does not... I do feel, however, that the Cirque model of performance (particularly that of actor-replacement within a role) can treat the clown filling the particular clown role into more of an automaton-gag-presenter... IE: "We want it this way, so do it this way - not how you want to do it. Do it how we want you to do it." It's directed more like theater than like Circus.

MODERNITY:
I'm excited to see a new crop of clowns being birthed out of a few key centers in the US: The Clown Conservatory in San Francisco, Dell Arte in Blue Lake, CA, the Celebration Barn, in Maine, and a few companies in New York. I'm sure there are more (I hope!) and I'd love to hear about them - but the young-clowns who seem to be getting steady work, seem to be those coming out of training programs. This seems to be not so much a direct result of job-placement via the school, but rather as a reflection of the accumulated circus-interest in those markets/populations.

Clown humor has also been adopted by cartoons and comic strips for the past 100+ years. "Calvin & Hobbes" portrays clown logic impeccably, whether Bill Watterson had any conception that he was doing so.

Clown-perception on the whole is pretty sad. The ubiquity of 3-ring circus-clown makeup on face-to-face birthday party entertainers, street performers and film-clowns has led to a great deal of stigma against ALL clowns. And frankly, I have sympathy for coulrophobes (those with a fear of clowns) because: the magic of a smile that can be seen in the furthest bleacher (and it is magical!) becomes a hideous self satire in person. At worst, it can stand for the symbolism of the "mere" humanity & fabrication behind symbols of youthful innocence. When a kid sees The Easter Bunny on a smoke break, Santa kissing mom, or a clown with a real mouth under their fake smile... what are they supposed to believe. 3-Ring makeup has it's place, but I feel that it does more harm than good up front & out of place.

And, to introduce a topic for another essay - the Underground Circus scene has elevated and cultivated a few fairly excellent clowns, most notably Leighton, of The Yard Dogs Road Show.

Anyway, I would love to hear about great clowning from all over the spectrum of circus and beyond. If the circuses are being co-opted, or spread thin, or cost too much, or do not present clowns with their ideal situation - Clowns are presented with the opportunity to create Clowning opportunities in their own image. THIS excites me - for it brings freshness to an already funny field/art/profession. The dedicated clowns can prosper and shake the face of art now, in the same way that the early silent clowns leapt from Circus & Vaudeville to the Silent Screen. Preemptive cheers to the shift that changes clowning and comedy forever! Clowns will always be in circus, but clowns can always be more.
- Nikolas