I really can't decide. Both are great.

Super Metroid.

Metroid Prime, but Super Metroid is also an amazing game! I wish we would just get a new Metroid game already..

I would say there are (for better or worse ) at least 2 styles to nearly every Nintendo 1st party title. 

Pikmin, Fire Emblem, Mario Kart, Fatal Frame, Smash Bros, Nintendogs, and Animal Crossing count in that?

Super Metroid. I dislike First person.

Fatal Frame isn't really 1st party made, but aquired. Even still, motion control camera vs analog stick gameplay.

Mario has 2D and 3D games (New Super Mario Bros Wii U vs 3D World)

Star Fox has games that are on rails flight based vs adventures based

LOZ has top down vs 3D based, as well as very cartoony vs more realistic texture based (even stylized cartoon vs anime style)

Smash Bros is characterized in competitive fighting vs party game.

Fire Emblem has hardcore vs casual (given the new option that characters are no longer dead forever) which is newly introduced

Mario Kart has motion controlled style vs analog control. Also the newely introduced Mario characters only vs all Nintendo IP character inclusion

Metroid is obvious

Pikmin is not one of these titles.

Nintendogs, I couldn't tell you, never played nor do I follow anything based on this game due to lack of interest

Animal Crossing is also not one of these.

I guess I wasn't really taking into account there lesser known titles like Nintendogs and Pikmin. But still.

So 8/11. 

You're really stretching it with Smash and Mario Kart. I'm inclined to be more lenient on Fire-Emblem despite it also just being an 'extra option' in one game. Too be blunt, its kinda like claiming Splatoon is two (or even three) games... 

Are they different styles between games? Yes. That is what we are talking about right?

How much of a difference is it between first person and third person metroid? Not all that much. I feel Kart and Smash are equivelant in difference. Try telling competitive Smash players Brawl and Melee are practically the same.

And as far as "just being an option in a game" for Fire Emblem, it still changes the entire fundamentals of the way the player approaches the game. 

Smash Bros doesn't change its obvious formula it just happens to support both styles of play; meanwhile Mario Kart's formula doesn't change that massively between motion controls, control pads, and control sticks. Metroid Prime 1 and Metroid Prime Trilogy's first games are the same game despite the control improvements; it would not be the same game in 2D with a constant third person camera. 

BUT I do accept I may well be misinterpreting your meaning; you often seem like quite a reasonable user so I imagine that is infact quite likely the error I am making.