I took down about 6 buckthorn trees today with my little piece of junk chainsaw (Poulan "Wood Shark"), a few of the trees were over 30 feet tall. These are some of the biggest on our property. It felt great. I am already starting to notice oak, cottonwood, aspen and even a few cedars struggling to get a foothold where buckthorn had previously choked everything else out. Fortunately, I have old growth (very tall) varieties of many other species, so if I can get control of the buckthorn, and stay on it, the other trees may really take off.
I am not really sure what a brush hog is, but I wondered if that would be helpful. The problem is that there are so many larger trees where the little buckthorn are, I didn't know if it was practical.