Thanks for your question! It's always hard to know for sure who will have side effects from a medicine and who won't, and what those side effects might be. We each seem to react a bit differently to medication, both from a desired effects perspective, as well as from a side effects perspective. All doctors can do is predict what might happen.
So, that is why treating disease is often a matter of trial and error, to some extent. There are many medicines that treat asthma effectively. But not all of them are effective for every person with asthma.
You don't say how long you've been using Symbicort. Often, side effects gradually go away over time, as you get "used to" the medicine. So, if you've just started taking Symbicort, if you hang in there, things might get better. However, if you have been taking it for a while and you're still feeling the side effects, then it might be time to discuss with your doctor the possibility of trying something different.
Advair and Symbicort are both in the combination class of asthma medicines. Both contain a steroid (to reduce inflammation in the airways) and a long-acting beta agonist (to relax the airways), but they each contain different specific medications of those types. For severe or medication-resistant asthmatics, combining those 2 types of medicines seems to produce better asthma control than when using either type by itself.
Symbicort contains budesonide (the steroid) and formoterol (the beta agonist/bronchodilator), while Advair contains fluticasone (the steroid) and salmeterol (the beta agonist). I can't say that one is better than the other, because they are so similar. Both also have similar possible side effects, but as to how you would react, only trying it will tell you for sure.
So, if you think that might be the course of action you should take, talk with your doctor about your options. After all, your doctor knows you better than I do!