That's a good question, and here's the answer.
The Las Vegas Circus Circus is the original and was opened in October, 1968 by Jay Sarno, who was also the brains behind Caesars Palace. When it debuted, the property was just a casino; well, when we say "just a casino", we mean a casino designed like an enormous big-top tent, with aerialists and a one-armed-bandit-playing baby elephant. In addition to the elephant and the acrobats, another element that was already in place on opening day was the white clown statue that still stands outside the property, which was commissioned by Sarno and designed by sculptor Montyne.
Not surprisingly, Sarno's dream of attracting high rollers never meshed with the circus theme and by 1974 he was broke. The casino was purchased by William Bennett and by that point the first of several hotel towers had already been added. Rather than ditching the circus theme, however, Bennet opted to stick with the family-friendly concept and use it as a draw for middle-income families. Two years after he'd purchased it, he had Young Electric Sign Company, responsible for much of the neon signage around town, design and erect the 123-foot "Lucky the Clown" marquee at the entrance. (As an aside, we came across some statistics in the course of researching this answer. We haven't been able to verify them, but we read that consists of 1232 fluorescent bulbs, 14,498 incandescent bulbs, and 3/4 mile of neon tubing light.)
Circus Circus Reno, on the other hand, came a decade later and occupied what was formerly a Gray, Reid & Wright Department Store -- the only department store in the state of Nevada at that time -- built in the late '50s. In 1977 the store moved to new premises and the owners were approached by CIRCO Resorts, then operating company of Circus Circus Las Vegas, who took over the property. It opened in July, 1978 after a year of renovations, and was modeled on its southern counterpart to some degree, but was the work of a different design team. We don't know who designed "Topsy the Clown," who's this casino's mascot, but we did read that he's allegedy the biggest clown in the world. You're right that he's in a totally different style to his Las Vegas counterpart, more like a Pierrot than a classic circus clown. If anyone out there has any additional information about who designed the Reno clown, we'd love to hear from you.