Brain age is a powerful marker of general brain health. Furthermore, brain age models are trained on large datasets, thus giving them a potential advantage in predicting specific outcomes - much like the success of finetuning large language models for specific applications. However, it is also well-accepted in machine learning that models trained to directly predict specific outcomes (i.e., direct models) often perform better than those trained on surrogate outcomes. Therefore, despite their much larger training data, it is unclear whether brain age models outperform direct models in predicting specific brain health outcomes. Here, we compare large-scale brain age models and direct models for predicting specific health outcomes in the context of Alzheimer's Disease (AD) dementia. Using anatomical T1 scans from three continents (N = 1,848), we find that direct models outperform brain age models without finetuning. Finetuned brain age models yielded similar performance as direct models, but importantly, did not outperform direct models although the brain age models were pretrained on 1000 times more data than the direct models: N = 53,542 vs N = 50. Overall, our results do not discount brain age as a useful marker of general brain health. However, in this era of large-scale brain age models, our results suggest that small-scale, targeted approaches for extracting specific brain health markers still hold significant value.