What determines what "view" gets displayed first on a page?
If you refer this Question on stackoverflow: How does Drupal Views decide between multiple displays with the same path, I think he has described both situations of views in his answer as separate paragraph and second paragraph is your answer. 

I am pasting the entire answer here of @Andrew Aledge,


  If you're referring to the display within the views: each view display
  has a position and the displays are loaded according to that position
  in an ascending sort. So if you create a page display (which may get a
  position of 2 since the Default display typically has a position of 1)
  and then create another page display after that, the next page display
  may get a position of 3. The customer will be exposed to the position
  it reaches first (2, provided that they have met the criteria).
  
  If you're referring to the views themselves: views are loaded in order
  of their view id (vid). The customer will be exposed to the first one
  loaded.


If you see the LAST TWO Lines, he has mentioned on which basic the views decide which view will be displayed and which one not. He means that Provided all conditions same, the view will be shown as per the view id(vid)

Other situation: Apart from above two situation, Which view user will see if they have different Roles. So in that can I think It will be decided based on which user has access to which view(I mean based on thier role access), and if same user has access to multiple views then in this case it will decided again based on vid.

I think, above three discussion have cover all the various situation of visibility of view.