If your grass is not very tall, you mow often, and there are no rocks or brush, the finish mower will do a prettier job, and pretty fast too. Plus, you can usually use a wider cut finish mower than you can brush hog with the same horsepower.
However, my experience is that if I let the grass and weeds get even 6" tall, the brush hog (Rhino SE5) is faster AND does a better job. By "better job", I mean it cuts the grass and doesn't leave any survivors, whereas the finish mower cuts beautifully to a point, but starts leaving survivors when it gets a little tough or tall.
I'd like to get to a point where I could always use the finish mower on my acreage, but frankly, the brush hog still always does a better job on most of it. Plus, I have areas back in the woods where I wouldn't think of using the finish mower. The result is that since I moved from town where I mowed a one acre yard with the finish mower, I really don't have much use for the finish mower any more. I am considering selling it or trading for some other implement.
I am happy with the cut the brush hog gives, especially when I don't let it get too tall between cuts, and hit it with an angle grinder from time to time. From a distance, looking out over several acres, there's not all that much difference in the cut. Get in the middle of it and look closely and you can tell the grass is a little taller and rougher cut than what the finish mower would do.
My wife uses the Craftsman for the acre or so "yard" and the rest is brush hogged. Our neighbors all use brush hogs too, even up next to the house. Of course this is no country club I live in, so you might not be satisfied with it.
However when we both mow on the same day, you really can't tell precisely where the Craftsman leaves off and the brush hog takes over.