An interesting question because both the ‘conditional’ element and the ‘repeated’ element of ‘would’ tend to collide in the second sentence. And that makes it difficult to separate them. In this sentence - If I saved my money, I would buy a car - there is no doubt that the conditional element is paramount.
Back to your question. Both sentences are fine and I would say that the difference is that ‘went’ states the action as a factual result of and ‘would go’ indicates the likely consequence of didn’t eat.