If i give you a simple difference 1. 읽어냈다-(" Oh Shit I did! I did read this book until the end!!holimoli!!) It can be an expression that you achieve some goals. in this case, you finish reading a book. 2.읽어버렸다.- "Hey man...I finished reading a book you recommended. I have nothing to read now..." It can be an expression that you did something and feel kind of regretting of doing it cheers DK

아/어/여 내다 is used when someone finish doing something by oneself and has feeling of hardship. 아/어/여 버리다 is used when someone finish doing something and has feeling of relief or regret. ex) 적의 침공을 막아 내다 추위를 이겨 내다 끝까지 참아 내다 동생이 과자를 다 먹어 버렸다. 약속 시간에 조금 늦게 갔더니 친구들은 모두 가 버리고 없었다. 그 일을 다 해 버리고 나니 속이 시원하다.