Maybe very little, or maybe longevity and reliability. We know Honda and Yamaha engines and inverters are excellent and quiet performers with few, if any, problems reported. Honeywell gensets are newcomers on the block, so we have to wait and see.
A similar question was asked about Boliy generators a couple years ago, and their track has proven to be dismal, with numerous problems reported and difficulties in getting parts and service, even under warranty. Supposedly has improved now, but... caveat emptor. Even so, some people bought the less expensive Boliy and got decent service from it, at a relatively bargain price.
Let's up Honeywell, a larger and more established competitor, can do better.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL