For cutting, I would go with the Anavar, every time. It's a DHT based drug, and does not convert to estrogen. In fact, the opposite, it will add to a harder, drier look. One of the main actions of dbol, that makes it such a powerful drug, is it's conversion to estrogen. While bulking, this added fluid will help with strength and pushing blood into the muscle. To cut off the action, would be to dramatically limit what dbol is capable of doing. 

Of course, we want to limit estrogen while cutting, as it will blunt your fat loss. Could you lose fat on Dbol? Sure. you can lose fat on any steroid, but it isn't going to be anywhere close to ideal