Is it true that a larger, representative dataset is always better to use than a smaller, representative dataset? By "representative" I mean that the data in the dataset faithfully reflects the "underlying signal" a model is trying to tap in to. Is it always true that, as long as increasing the size of the dataset has not added bias, ie it is still just as representative of the underlying signal as the smaller dataset, that the more data the merrier for the model?
What does it mean if a dataset has a higher accuracy on a smaller dataset? Is that a sign that it's overfitting on the smaller dataset, not that it's a better idea to use the smaller dataset? Should it be expected to do better or worse than a larger dataset?

I'll interpret "representative" to mean "obtained without bias" such as selection bias.  The question is then "is more data better than less?".
Assuming the data are a simple random sample from the appropriate population, then more data is usually better in so far as power, precision, etc are concerned.  From more data, we are better equipped to model the conditional mean since we can spend more degrees of freedom (say, expanding the effect of some covariate using restricted cubic splines).  However, there are non-statistical considerations we should highlight.
Randomized control trials (RCTs) often intend to use "enough" data.  Too little, and the RCT may be under powered, but too much would be a waste of resources.  Closely related to this consideration is the relative need for the additional precision; does matter if I can estimate the uncertainty in the effect to 8 decimal places?  Its probably more important in say nano-technology than it would be in social science.
