Does the average accountant get paid more than the average software engineer?

No... but the exceptional developer can earn more than the CPA.  It is tougher to pass the certification tests as a CPA.

One thing that benefits an average CPA (and not necessarily an average accountant) is the certainty of the tax season while there is no certainty of income for an engineer.   For average CPAs,  tax software answers most questions. The certainty of income from preparing tax filings between February and April may carry an average CPA through the rest of the year without the need to work the average 40 hour/ week that an average engineer would have to be working.   Engineers, on the other hand, need to constantly update their skill set or they may fall behind "an everage".    I would also say that if an average CPA is decent at communication and decent at tax work, he/she would be getting referrals from his/her clients without putting much effort into marketing.   An average engineer hardly would get as many referrals and probably would have to keep looking for jobs and reaching out to employers or to parties hiring contractors. One thing that works better for (freelance) engineers is that an average project is of a higher value than an average tax engagement for a CPA.  An av engineer may have 5- 7 projects / year @  $8-20k each while an av CPA may have 40-100 clients at $300-1,500 each.

Probably not. However, other questions are more important. What is the salary distribution? If you obtain a degree in accounting are you more or less likely to be employed in the field than a person with a software engineering degree? These average earnings statements mattered in the '80s and '90s when getting a degree virtually guaranteed you a job in the area you studied. Now it guarantees absolutely nothing. You have to look at many other factors and take your best guess about what conditions will be like when you graduate. Break out the crystal ball, if you have one. Quick note--other answers are comparing software engineers to CPAs. Most accountants are not CPAs.

No. The average pay for a Software Engineer is $72,722 per year, see http://www.payscale.com/research/US/Job=Software_Engineer/Salary while the average salary for a Certified Public Accountant (CPA) is $56,406 per year, see http://www.payscale.com/research/US/Job=Certified_Public_Accountant_(CPA)/Salary.