Both work. They work on different machines, for different sellers, at different times of year. Picking wrong is what costs money.
Auction wins when demand is deep
Common, in-demand machines — utility tractors with loaders, skid steers, good hay equipment — do well at auction because several buyers want the same thing on the same day.
Auction also wins when you need a certain date. It sells on the day it sells, which matters if you are retiring, moving or settling an estate.
Fixed price wins when the machine is specific
Specialty equipment, odd sizes and anything that needs explaining does better with a price on it and time to find the one buyer who needs exactly that.
Fixed price also lets you hold your number. At auction, two slow bidders on a rainy Tuesday set your price whether you like it or not.
Count the real cost
Auction cost is commission plus hauling plus any listing or cleanup fees, and it comes off the top.
A fixed-price listing here costs nothing to post. The cost is your time answering messages and the patience to wait for the right buyer.
Timing beats both
Hay equipment sells best ahead of hay season, not after it. Tillage sells in the spring. Loaders and blades sell when the weather turns.
A machine listed in its season, priced honestly, with good photos, beats the same machine dumped at a winter auction almost every time.
A reasonable middle road
List it at a fixed price first and give it a few weeks. You keep control and pay nothing.
If it has not moved and you need it gone, run it as a timed auction with a reserve you can live with.
List your equipment
Free fixed-price listings, or run a timed auction with your own reserve. Sold AS-IS, WHERE-IS, WITH ALL FAULTS.