I actually feel like someone like Patti LuPone, whose work and fame are primarily in the theater, may demand a higher salary than someone like Catherine Zeta-Jones, who can afford to work in the theater for a smaller paycheck because she'll make so much more than that on her next film project.
A list movie stars earn many millions of dollars to star in a movie. What CZJ considers "a smaller paycheck" is still more than what many people earn in a year, and more than what even the biggest "Broadway names" earn.
Big name stars often get a percentage of box office on top of their salary, so in a hit show, that could be a substantial increase.
Generally, lead contracts include a raise for Tony nominations and another raise for Tony wins (for the performer, not necessarily for the production), but that is all part of the negotiation.
Another thing to consider is the number of stars and/or leading roles. A show like Wicked has two leads who are usually on the same level of fame, whereas a show like Gypsy usually has one star: Rose. Lane and Broderick may have earned $100K per week as the two stars of The Producers, but I'd be willing to bet they received less for It's Only a Play, where they shared billing with an entire cast of huge names.
Bottom line: outside of the minimums required by Equity, there are no rules when it comes to salaries, from person to person or show to show.
Nothing matters but knowing nothing matters. ~ Wicked
Everything in life is only for now. ~ Avenue Q
There is no future, there is no past. I live this moment as my last. ~ Rent
"He's a tramp, but I love him."