I cut a lot of property (neighbors) that has 1" size trees and larger brush. Brush hog is the way to go - any decent unit will do 1" stuff without much drama. I used to use a 7610 (smaller Kubota) and a light duty 4' brush hog and never had any problems or issues if I stayed around 1". I now use a med duty 6' unit on a MX5100 and never even pay attention to stuff that size.
Also look around for used stuff , you often see good functioning units that are not pretty but are mechanically sound for a very reasonable price! Good luck