Fit both hierarchies to the historical data and compare their posterior predictive checks. Use discrepancies sensitive to between-individual tails, such as the maximum standardized personal mean, tail counts and the spread of individual sample means. Simulate new individual means as well as repeated observations; conditioning only on fitted personal means would conceal a poor population model.
Leave whole individuals out for cross-validation, rather than just measurements, when the aim is prediction for a new individual. Compare held-out predictive log densities or interval calibration, with uncertainty in the comparison. Check both fits' Markov chain Monte Carlo convergence diagnostics and sensitivity to scale priors. Better tail prediction and adequate calibration would support the heavier-tailed model; the data are required to decide, so no empirical winner can be asserted here.
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