IMHO, most lawn equipment probably would not benefit from either of those over a quality Dino oil.. but if I had to choose between the two you mention, then HM Dino.
Honestly, if I needed some oil for a gas-powered lawn more, I'd probably be just as well off taking the used oil from my car and using it in my mower, considering the overall light load placed on it while mowing the lawn.
Don't overthink this.