Is it unusual to owe more state income tax than federal income tax?

It depends on what you mean by "owe."

If you mean the amount you have to pay at the end of the year in addition to your withholding, it is not at all unusual. The amount withheld is only a rough estimate of what you might owe in taxes and controlled by the W-4 form and the equivalent state form. Few people know how to accurately fill out either form, so all sorts of funny things happen.

If you mean your liability before withholding, it is kind of unusual, since generally state tax rates are much lower than federal rates. But the federal government does have all sorts of tax breaks for low income filers (EIC, child tax credits, etc) that can sometimes eliminate or nearly eliminate federal taxes, so it is quite possible for that to happen.