Heinz is the single dominant force in the ketchup market today. It has no serious competition, as I learned from reading the intriguing snapshot and history of the ketchup industry yesterday in the New Yorker's article, The Ketchup Conundrum. (Thanks to tsutanai for posting the link.) That it has no real competition is certainly not for lack of trying. French's mustard had a similar monopoly on mustard in the U.S. in the late '70s until Grey Poupon successfully advertised its product to customers who realized just how good the mustard was.
The article details a multitude of factors and intriguing studies, including the science of successful taste and that Grey Poupon is made in Connecticut from Canadian ingredients. I hadn't realized that it was only within my lifetime that the important of variety in an edible product line became the modus operandi. Prego made a killing when a visionary and food surveyer named Howard Moskowitz helped them to realize that there was no one perfect pasta sauce, and that the niche of "Extra Chunky" was entirely unclaimed in the pasta sauce market. And that there is only perfectly taste-balanced ketchup, and it has the market completely sewn up.