The lawn tractor would probably cut twice the width of any pusher mower and do the cutting at greater speed, meaning quicker job completion, so if you are charging by the HOUR you lose money vs. using a push mower. But if you are charging by the JOB, you will earn more because the lawn tractor will let you work faster.
I do not understand how one would lose money on an hourly rate with a rider. If you charge $30 per hr, as an example, and it takes you 30 min to mow, you earned $15, but that's more time to mow another job. Now if you charge $30 to mow, regardless of time then you may or may not make money. If you charge $30 for the job and it took you an hour and 15 min then you lose money, vs. an hourly rate of $30.
To me, best of both worlds is bid both ways, by job or hr, but hourly rate is higher. Any time I have had work done, that's how they do it, usually they will go hourly for the first time, then quote you a flat rate there after.
To the OP
It depends on how much you have to pay for the rider, vs the push mower and cost for fuel and maintaining them. By the way, if I were going to do it as a business, I'd at least get a self propelled push mower. You will really come to love them on hilly lawns.
Most likely if you get busy, and a variety of jobs, you'll end up needing both. Iff you are doing mostly homes with the 1/4 acre lots, I'd get a self propelled walk behind, and invest the difference in trimmer equipment.
