The simple question, IMO, is whether Doty was correct in ruling that Goodell violated the law of the shop. It seems fairly simple. The NFL's argument basically is (as has been said already) that Goodell has the power to issue whatever penalty he wants. That even if a federal judge thought the penalty is outrageous, or that Goodell shouldn't have issued ANY penalty at all because there's no evidence of wrongdoing, that none of that matters because the CBA grants Goodell this power.
The NFLPA's position is that yes, within reason, Goodell has the power to issue penalties for wrongdoing. But Goodell can't simply do WHATEVER THE HELL HE WANTS. The rulebook has penalties listed for a reason, and while Goodell indeed has some latitude (like a judge fining a person $500 instead of $100 for a speeding ticket), he can't simply issue ANY penalty. That is, if the rulebook says football tampering is a $25,000 fine, Goodell, while being granted some latitude to increase that, can't just suspend Brady for three seasons for that. In other words, the NFL's argument that Goodell can do whatever he wants is fundamentally flawed and even the CBA is governed by US Labor law.
Given what we know of the case, I can't see how the NFL wins this. Goodell clearly is way, way, way out of bounds with how he handled all of this.