Admittedly I don't know but a quick google suggests it can vary quite a lot from generally feeling unwell, tiredness and coughing to full on fever and weight loss. Also I would expect it affects cattle differently to humans.
Wiki says that the treatment for active TB is one set of drugs for 2 months, then a different set for 4 months. To me that suggests that you are physically ill for 2 months, then have 4 months of drugs to stop it spreading and to stop it returning.
If the cow could talk, I think it would prefer 2 months of being ill to being killed. So if the owners want to pay for treatment, can ensure that it will be quarantined for the correct amount of time and the animal is not in serious pain I don't see why the animal should be put down. Based on the BBC article it sounds like the owners are quite willing to do this.