• What makes the two distinctive?

It's a little different when discussing games, but in other media linear narratives are portrayed in the order in which they occur, whereas nonlinear narratives aren't. It's like the movie or show that starts at the end, then goes back and fills in the events to how things got there, or something that alternates between two different time periods. Star Wars is linear. Pulp Fiction is non-linear.

In games it seems that people use linear to describe a more guided experience where you move from one objective to the next, stage to stage (Call of Duty campaign is probably the best example). Non-linear is something that gives you the freedom to do things in a different order, make choices that change the game. Elder Scrolls is probably the easiest example of that.

• What are the Pros & Cons of the two?
• Which has more appeal?
• Which is easier to do?
  

As a writer or a player? I guess I'm going to lump all these together into my opinion.

As a writer, I prefer linear because it's much easier to work on. I'm currently working on a project that actually has pretty minimal choices and paths, and my Articy screen gives me a headache every time I open it. One conversation in one scene with one character has like six different branches that I need to close off and loop back around and make sure it's all entertaining for the player to read. Then I have to factor in how this one conversation affects character and faction relationships, if it changes any decisions in the story and what mission options are available, etc.

As a player, I also prefer linear games because as much as I love gaming I find I have less and less time for it. I want to experience a game and actually be able to finish it before I die. Contrary to what the AAA industry seems to think, every single game that comes out doesn't need to be a huge open world full of pointless side missions. I think the newest God of War found great a balance of open areas and exploration while still telling a tight and focused story.