"the river flows" vs "the river runs"
Is there any difference between these two verbs when it comes to "rivers"?

Example:

The river flows / runs through the valley.

Question

"the river flows" vs "the river runs"
Is there any difference between these two verbs when it comes to "rivers"?

Example:

The river flows / runs through the valley.

Answer

It's mostly a stylistic choice based on how each word sounds.

Answer

I would use 'to run' for water, and 'to flow'  or 'to go' for rivers and alikes.
Using 'to run' for a river will emphasize something. 
Only the Author  knows whether there is some meaning to be emphasized.

Answer

Have you ever heard this song: The ballad of Easy Rider ?
First lines run like this:

The river flows
It flows to the sea
Wherever that river goes
That's where I want to be
Flow river flow
Let your waters wash down
Take me from this road
To some other town
... ...

This is the BEST version: https://www.youtube.com/watch?v=3dvBjKr2LcY
it starts at 35 min. 30 sec.
Hope you enjoy this song!