If you're an asthmatic, how do you tell the difference between an asthma attack and a panic attack?

Not easy. It can certainly result in a feeling of panic if you cannot breathe because of an asthma attack. So it is important to have a doctor examine you during an attack. By the exam or by testing it can be determined which came first. For instance, with asthma the doctor would probably hear wheezing during your attack. The oxygen level in your blood might be low.
Evaluation. At the time of symptoms, a physician examination can reveal the etiology. For example, if you are wheezing and desating during the symptoms, it is likely asthma. If your lungs are clear and your oxygen sat is normal, it is likely anxiety. Pulmonary function testing while the symptoms are present can also be useful in telling the difference.
With panic attack... ...People usually take deep, rapid breaths. In an asthma attack, breathing out is slowed down by the obstruction; it looks like trying to breathe through a straw.
Peak flows. Measuring your peak flows will help. In an asthma attack your peak flows will be affected but they won't be affected in a panic attack.