According to the dictionary I use to study, both are adverbs and their definitions are so similar that I can't tell the difference:
結局【けっきょく】: after all; in the end; ultimately; eventually
とうとう: finally; at last; ultimately; in the end
What is the difference between both words (e.g. meaning, nuance, level of formality, style of speech, none at all…) ?
「とうとう」implies a continual process that led to the outcome, whereas 「結局」doesn't.
For example, one can say 「結局力不足なのだ」but not「とうとう力不足なのだ」because 力不足 is not a state achieved via a continuous process. On the other hand, one can both say「とうとう力尽きた」and「結局力尽きた」which has roughly the same meaning, but the former draws a lot more attention to the continued struggle that led to the outcome.
Other examples:
Natural:「結局牛肉は好まれない」
Unnatural:「とうとう牛肉は好まれない」
1st:「少しづつ侵食が進み、とうとう倒壊した」
2nd:「少しづつ侵食が進み、結局倒壊した」
Both have very similar meanings, but the 1st describes how the gradual process eventually led to the outcome. The 2nd describes what the ultimate outcome was.
