stability or accuracy in making model, which one is more important?

I know that both stability and accuracy of answer are important in making model, but if we just have the option of choosing one of them then which one comes first? By my view, when we have unstable but enough accurate solution ( a solution with oscillation) , always we can get right answer by mean of unstable values. But when our model answer converges to inaccurate answer then there is no opportunity to find the right answer.