pineapplegame:

The difference between these two structures has always confused me. My TOPIK textbook attempts to explain the difference, so I’m going to go by their explanation!

V더니

   –    The subject is usually not in first person*.

   –     Used with a verb or an adjective.   

   –     First clause, even when in past, does not use past tense.

1. Highlights the difference between two contrasting phrases.

지난 겨울에는 눈이 별로 안 오더니 이번에는 많이 오네요.
It hardly snowed at all last winter, but this year it’s snowed a lot.

2. The result (second clause) of someone else doing something (first clause). The subject of first and second clauses are the same.

지난 주말에는 춥더니 이번 주는 따뜻해요.
Last week it was cold, but this week has been warm.

내 동생은 수영을 하더니 식욕이 왕성해졌다
My dongsaeng went swimming, so he had a huge appetite.

V았/었더니 –

     –   The subject is usually first person.

     –   Used only with a verb, not an adjective.

1. Used when you realize or notice something (second clause) after doing something (first clause).

오랜만에 고향에 갔더니 많은 것이 변해 있었어.
When I visited my hometown, a lot had changed.

2. The result (second clause) of doing something (first clause).

어제 술을 많이 마셨더니 오늘 머리가 아파요.
I’ve got a headache because I drank a lot yesterday.

내가 공부를 열심히 했더니 성적이 올랐다.
Since I studied hard, my grade went up.

*The Korean Grammatical Forms site says that Koreans sometimes break the “no first person on V더니” rule.