Here's the difference:
1. The "would" construction can only refer to repeated habits and actions in the past, not to states. So, for example, you can say either "When I was a child I used to play with my friends" or "When I was a child I would play with my friends". You can also say "When I was a child I used to live in the countryside", but you can't use "would" in this case, because it is not a habit or action.
2. The "would" construction is more literary, formal, 'educated' and old-fashioned. It is not commonly used in everyday conversation. It appears in all the grammar books, but - to be honest - I don't think it's a very useful construction for most students. You can live perfectly well without ever using it.