I think the most accurate salary data that can be considered for comparison would be taxable wages reported on a W-2, for software engineers with different titles at different companies. The wages would be much more representative of the total compensation package an engineer gets, as it includes salary, taxable equity, bonuses, and other benefits such as health care reimbursement, relocation, etc. Since the amount is for taxable wages, I think it would also more realistically account for vesting and other special situations such as deferred compensation. Provided that the data had a large enough sample, it would include a nice cross-section of employees at different parts of their vesting lifecycle with different types of equity compensation, and thus the numbers in aggregate would be useful for comparison.
Practically, the only entity I can see doing that type of study would be the IRS, or perhaps Turbo Tax or some other tax software vendor that adds some sort of anonymous wage collection option for users when filing. That actually sounds pretty creepy and intrusive though, so hopefully nobody at Intuit or the IRS is reading this and gets any ideas!