Doesn't it depend on how different their values are?

As an illustration, let's suppose each politician has a general competence score 0 <= C <= 1, where 1 means they achieve exactly what they stand for, and 0 means no better than random (e.g. a rock).

The other important factor is how much overlap there is between your preferences/values - suppose that the magnitude assigned to an issue scales with how much you care about it. Let's define the value overlap as 0 <= V <= 1, and the proportion of issues you disagree on as (1 - V).

Then the net movement toward your preferences this politician achieves is: V * C - (1-V) * C = C * (2V - 1)

So as long as V > 1/2 (i.e., you agree on more than you disagree on), more competence is a good thing. For example, I'd rather have someone with whom I agree with on 80% of the issues and is 80% competent, than someone with whom I agree with 90% of the issues and is 50% competent.

We don't tend to argue about issues where there is strong value overlap (for example, no one's going to come out explicitly in favor of bribery, or executing innocent people, or another recession), but politicians can still make a difference on these issues, so I thing there's strong reason to suspect that V > 1/2 for most politicians.

Of course, not every failure to achieve a goal is due to honest incompetence. If a politician intentionally speaks in favor of a policy with no intention of carrying it out, measures of general intelligence like GPA or IQ should not be as good at predicting this kind of "incompetence" as they should be at predicting honest incompetence. However, more specific measures of competence, like a politician's past record, should be helpful in predicting how effectively current promises will be kept.