いえ sounds more formal than うち. (うち is more colloquial.) いえ means "house" and うち has more meanings, "house", "my house" and "my" depending on the context. Examples: Please come to my house. = わたしのいえにきてください / うちにきて(ください)。 my mother = わたしのおかあさん / うちのおかあさん my friend's house = (わたしの)ともだちのいえ = (わたしの)ともだちのうち I hope you get it.

From the way I had it explained to me the difference between uchi and ie is the difference of using house or home in English. Uchi would be a warmer, more familiar and comfortable place were as ie is more formal and stiff. Hope this helps you.