I'm not aware of any statistics that set forth which major insurance company denies the most claims, whether in terms of total claims denied, or as a percentage of claims denied as compared to claims filed. Any such statistics might not be entirely helpful.
For example, the largest car insurer in Maryland is well known for "accepting" responsibility for a claim, but refusing to pay any compensation for personal injury, because the claims adjuster "finds it hard to understand" how someone could get hurt in the subject car accident.
Presumably, such a claim would not show as in any study as a denied claim, although the injured person who received nothing would certainly disagree with that conclusion.
The study that I'm aware of was conducted by the American Association for Justice several years ago. Their well-reasoned analysis concluded that the 10 "Worst" Insurance Companies in America were: