There are no absolutes, both words have several meanings, and the meanings overlap. However, we can say this:

"View" emphasizes us, the people who are looking.

"Scene" emphasizes what we are looking at.

(By the way, it is a complete coincidence that "scene" and "seen" sound alike (are homophones). They are completely different words. There's no connection between them).

I might say any of these things:

a) She has a wonderful view of the Rocky Mountains.

b) Her house has a wonderful view of the Rockies.

c) She posted a picture of her wonderful view of the Rockies.

d) The view from her window is awe-inspiring.

e) Through her window, she looks out on a spectacular mountain scene.

f) The scenery around her house is stupendous.

g) A panoramic scene of the Rockies surrounds her house.

h) She has a scenic view of the Rockies.

I can also say this, even though it doesn't fit what I said:

i) Through her window, she looks out on a spectacular mountain view.

But I couldn't say any of these things (although they would be understood):

a) Her house has a wonderful scene of the Rockies.

b) Her house is surrounded by magnificent mountain viewery. (Viewery is not a word).

c) A road sign said "Scenepoint Ahead."

Scene would be used for either a scene in a movie/play or for describing the atmosphere of something. 

"In the next scene, the actor trips."

"That bar really wasn't my scene. Too loud."

"It was a horrific scene."

However, "scenic" can mean beautiful to look at. 

"The boat ride was very scenic."

View would be used to describe what you are looking at, what you can see.

"The balcony has a lovely view!"

"Look! We have a view of the park!"

This is somewhat off-topic, but it's a good play on words.

Denali, the great mountain in Alaska, is often hidden in fog. Tourists, hoping to get a view, board the tour bus that takes them into the park. Unfortunately, it fogs up. By the time they get within viewing distance, there is nothing to be seen. The tour bus drivers says,

"I'm very sorry, folks. We have missed the view, but we can view the mist."