Three axles mean a lot more wear on tires. You also have to be very careful with inspection stations. Let's say you have ten ply tires and they're rated at three thousand pounds each. Your axles are rated for twenty one thousand pounds but your tires are only rated for eighteen. /forums/images/graemlins/blush.gif
A lot of three axle trailers run on axle as a non brake. The seven thousand pound brakes are a lot smaller than those on the ten thousand pound axles. So you could be running less brakes, ie, more risk.
If you're towing with a single axle one ton or a three quarter ton then a three axle trailer can share the truck spare saving you carrying a separate spare for the trailer.
A dually or one ton with eight lug wheels will share tires and wheels with the dually trailer.
I'd go with the dually. Bigger brakes, more rubber, and ten ton is a lot of weight back there when it gets a mind of it's own.