Short answer
Both can hold a license. An LLC offers flexible management and pass-through taxation with lighter formalities, while a corporation has a board structure and is taxed at the entity level unless it elects S status. For licensing, the bigger effect is who you list as control persons, since regulators run disclosures and background checks on them.
The license type is set by what your business does, not by your entity. What the entity changes is governance, taxes, and who the application treats as a Control person. An LLC lists members and managers; a Corporation lists officers, directors, and major shareholders. Background checks and disclosures follow those people.
Confirm the tax side with an accountant or attorney, then pick the structure before you file so the application matches your formation documents.
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