I asked my college who used to be a Korean teacher about your question. He said that people use 으니(까) to emphasize or stress on the "reason clause", 아/어서 is usually used in normal case. I used to live in Korea and study Korean. As far as I remember, most of the time I used 아/어서 in my daily conversation.

Look at these google results and you'll find plenty of information about the difference: http://bit.ly/1kcBlpw Also check out the lessons at talktomeninkorean.com where they talk about both 으니까 and 아/어/여서. http://www.talktomeinkorean.com/lessons/level-3-lesson-7/ http://www.talktomeinkorean.com/lessons/level-5-lesson-14/