Levothyroxine is T4 (a bio-identical copy of the T4 your thyroid made). Synthroid is one of the brands of levothyroxine, Levoxyl and Unithroid are other brands. There are also several (around 8) generic producers. The key is consistency -- if your pharmacist can always get generic T4 from the same source, that usually works as well as a brand and can save money. If not, then there may be fluctuations in the response to the T4. In general it is recommended to "protect the brand" to ensure consistency.
I'm not a doc but I can tell you that if generic is taken that of times you will experience differences in the body. Though generic has the same meds, the filler that is used to bind causes the medication not to be absorbed properly in the body and thus causes flux in the way it's suppose to work.
Ask your pharacist. I've been on Levoxyl 125mcg for over 10 years. The two times my physician tried to switch me to Levothyroxin, was bad news for me however, I have 1/2 a thyroid and I do not know your condition. Something to think about though.