I use both, and differs with the application. I have used 6' chain with steel J hooks on every wheel, just recently I purchased two 31" straps for the front axle to keep from scratching and then 2 J hooks on the backhoe mounting plating. New York is a every wheel chain tiedown plus strapping your loader and backhoe bucket down to the trailer also. I chain and strap like I did hauling steel, you can never use too many hold down devices.
Speaking of this, hauling wasn't my problem two weeks ago, I drove to my daughters house in Brunswick with my new YT235 Yanmar to pull out posion Sumack trees probably 30 or so. She lives on a hill in front of her home like 30 degrees, I parked facing down hill on the oncoming side wheels turned towards the grass. Unchained tractor, started and proceeded backwards, I had the sensation of really flying in reverse but I was mistaken. The rear tractor wheels were on the beavertail at the time of the speed sensation, the pickup truck back wheels were up in the air rolling forward on the front tires.
The whole truck, trailer, and tractor were rolling down the hill with the front tires turned the unit jackknifed on the neighbors lawn with the trailer jamming into truck bed smashing it into the frame. Thank goodness it did, or more damage would have ensued. Lesson, always chock all of the wheels, never unload on a hill, and lastly, put the truck in 4 wheel drive. Four wheels in park would have been a better situation. After one week, my son fixed trailer, and changed tire sliced by head rack, luckily the brand new tractor wasn't hurt or damaged, but, when I reloaded the trailer, I loaded it up on top of the hill on a flat surface all blocked up. I'm in the process of adding crank jack's on the rear to control the weight compression lifting the pickup truck. I feel foolish for admitting this, but if I can give someone pause before they make a mistake and get hurt or killed and prevent damage.