This is the distinction between the centered and non-centered parameterizations of hierarchical models. The short answer is it depends on how much information there is in the data to pin down the parameters, but I often find the non-centered (your second option) to be a good default. More details: 22.7 Reparameterization | Stan User’s Guide
In general it’s easier for the sampler for parameters to be on similar scales, so I would say it’s usually better to do the second option and scale them up by different amounts, with the raw parameters N(0,1).
I think the advice that parameters be on similar scales applies in general, so same for the non-linear case.