First person provides an insight into one character. Many readers are turned off by only seeing events through one character's eyes. However, I believe, with the right character, first person can be really engaging.
His Hope, Her Salvation is written in first person. It's told from the perspective of the hero. This was a challenge for me as a writer, but I felt it was crucial that the story be told from his point of view to fully appreciate the care with which he approached the heroine.
The story is told from the perspective of one or more characters in third person. This can be done in many ways.
The advantage of this over first person is the reader can be given additional information crucial to the story without being limited to the information available only to the main character.
His Ship, Her Fantasy is written like this because I felt the style drew the reader more into the action.
One Character - One Scene
Each scene is told from the third person perspective of one character. This is a great way of showing how scenes affect a character and helps evolve character-driven stories.
There are writers that can write a scene that provides multiple perspectives. However, I am not one of them. I find it distracting. The most effective execution I've seen is where the head hopping occurs at paragraph breaks. Done properly, it appears almost seamless.