Benefits of the stack-based Finite State Machine implementation

I'm developing a 2D game for my final course assignment (term paper), showing the best techniques of the game development, design patterns, different algorithms and more.

I haver never developed a game before and I'm struggling very hard to design a game engine that involves the best practices of the design patterns.

For the game state management (intro, menu, loading, playing...), I decided to use a FSM. There's a state design pattern and finite state machines using stacks. Are there any benefits using one or another? What is the mostly used approach?