The most significant differences between an LLC and a Corporation is in a) structure and b) governance. Generally speaking, the way a Corporation is structured and run is well-defined with little room for variance. An LLC is structured and run by a contract between the LLC and its owners (Members), which makes it very fluid and adaptable. A Corporation is very rigid – the way in which it is set up and run is defined by law and practice, so there is little room to change things. The benefit of a rigid structure is predictability – everyone involved (investors, lenders, advisors, employees, etc.) knows exactly how a Corporation works. This rigid Corporate structure is also highly scalable.
An LLC, however, is a much newer type of entity, and it is designed to be very flexible. The state laws and rules that define LLCs are typically very broad – and purposefully so to allow for variation. The LLC can be structured, governed, and taxed exactly like a Corporation, but can be set up for the Members (owners) to run the LLC directly, without a board. The roles can be defined by contract (Operating Agreement) between the LLC and its Members. The obvious benefit is that an LLC can be tailored to meet the exact needs of a specific business. The drawback is that, since the baseline laws are broad, the governing documents (e.g. Operating Agreement) must be very well done to avoid surprises.