Despite the vaunted problems at Yum! Brands' (YUM 0.40%) KFC chicken chain in China, the fast-food operator's Pizza Hut chain continues to slice its way to gains, a testament to the global appeal of pizza itself.

Were it not for its KFC woes, its parent could be a stellar performer; but because it derives two-thirds of its revenues from China, the disaster that followed in the wake of the avian flu outbreak and its suppliers injecting chickens with antibiotics, has caused the downfall to be magnified. 

Yet, where Yum! has seen an unrelenting decline in same-store sales at its chicken restaurants, the pizza chain maintains strong growth, with comps rising 10% in October compared to a 5% decline at Pizza Hut, which followed a September in which sales were up 6% and down 13%, respectively. Although Yum!'s pizza business isn't quite so robust here at home, with comps down 1% last quarter, both Domino's Pizza (DPZ -0.48%) and Papa John's Pizza (PZZA 1.15%) have done better.

Continuing its turnaround efforts, Domino's experienced 5.4% growth in same-store sales in the U.S., and 5% growth overseas, helping to generate a 19% jump in profits. Similarly, Papa John's witnessed an 18% rise in profits, as comps rose almost 2% here at home, and over 8% internationally.

No matter how you slice it, the pizza business is hot. But it's becoming more than just a place to drop in and grab a quick bite, as pizza joints want to capture more of the fast-causal dining dollar just like their burger brethren. Just as we saw Wendy's and Burger King Worldwide remodel their restaurants to make the dining experience more relaxed, we're seeing the humble pizzeria go through a similar transformation, too.

Sbarro, perhaps best known for having a pizza shop in just about every mall in America, is going for a more refined atmosphere with new, higher-premium restaurant Pizza Cucinova, where it will serve artisanal Neapolitan-style pizzas with flour imported from Italy and ingredients that include wild mushrooms, white truffle oil, potatoes, and gorgonzola cheese. Between the mall operation and this fine cuisine experience, it also has plans for mid-tier Sbarro Brooklyn Fresh, which is probably more akin to the Chipotle Mexican Grill concept than anything else.

And that's where pizzeria owners see themselves heading. There's been a mass explosion of these high-minded-concept pizza shops that are trying to recreate the Chipotle experience in a pizza joint, such as Blaze Pizza, Pie Five, and PizzaRev, a project that's got financial backing from Buffalo Wild Wings, which itself is trying to expand its brand concept.

Despite all the happy talk and yummy ingredients, I'm not certain whether this has legs. Pizza Hut already offers a fast-casual dining experience, and its sales have lagged. Rival Pizzeria Uno ended up going into bankruptcy a few years ago as sales faltered, and it thought the way to grow again was to head toward the quick-serve model. It ended up opening hundreds of Uno Express stores.

I'm not sure that, when it comes to pizza, we want more than just the quick pie we can pick up at the local pizzeria, or have delivered to us by Domino's and Papa John's. If I were going to invest my money in more than a simple slice of the market, those are the two I'd call up for fresh, hot delivery to my portfolio.