The difference between i.e. and e.g. is as follows:
i.e., an abbreviation for the Latin phrase id est, roughly means "that is."
e.g., another Latin abbreviation, stands for "exempli gratia," roughly meaning "for the sake of example."
"That is" should be used for specific clarification. When you want to add information, you use i.e.. You can use i.e. for lists, but only if you're writing the entire list.
When it comes to badgers, I like them in my house—i.e. (that is), I have several pet badgers.
In order to keep a pet badger, you need to possess specific qualities; i.e. (that is) patience, kindness, and thick leather gloves.
In the above instance, "that is" works fine, because it's specifically clarifying what I mean.
In a case like this, though:
I love my badgers, but they've given me some problems in the past (e.g. scratches, bites, and horrifying night terrors).
...there's more to the story. If the badgers also ruined the furniture, mauled other pets, and peed on the carpet, "e.g." would make perfect sense. If they only did the things listed in brackets, you'd use "i.e.."
TL;DR: "i.e." is very specific. With "e.g.," there's more to the story.