Davus,
I'll take a shoot at your question even though I don't use a finish mower. From what people have said in the past, a belly mower will cut down some field grass, but may take several passes the first time. IF you are looking at any small trees, stumps or rocks, you don't want to use a belly mower. Now a rotary mower will take on all of that and more. It will also cut your grass, but it will be a choppy type of cut. In some areas a rotary mower is called a shredder because it beats thing apart as it cuts them. That is great for fields and not as pretty for fine grass.
Hope that helps some.
MarkV