Closest thing to a heuristic is trying the task with non fine-tuned models and building an intuition for how far off each model is, what directions it's off in, and how easily you can improve that direction via fine-tuning.
For example, for classification, if is hallucinating semantically similar, but not technically valid classes, you can probably fine-tune your way out of the gap with a smaller model.
But if your task requires world knowledge, you likely need a larger model. It's not cheap, efficient, or generally useful to fine-tune for additional world knowledge directly.