You're right, it can be a big difference. However, gross income is a standard that puts all at the same point to start the process of looking at your financial picture. Payroll deductions vary widely -- taxes, medical insurance, life insurance, retirement savings, flexible spending accounts, wage garnishments, etc. Others pay all or most of those items on their own, not through payroll deduction. Starting with net income creates too many variables of what other expenses have or have not been accounted for.
You may be *approved* for a higher amount based on gross income -- but you may only feel comfortable with a lower monthly payment. But it is up to you, the consumer, to know your own needs/expenses. I wouldn't rely entirely on an internet-based calculator; good old fashioned pencil and paper, listing out your expenses then see how that compares. Be sure to include expenses that occur less often (insurance payments, car registrations/inspections, taxes, etc.)
Good luck with the house purchase!