For modern film emulsions, and for paper, hardening vs. non-hardening doesn't matter.
For X-ray films, it might -- though generally, if you scratch that it's before the fixer step, so the hardening fixer won't help.
There are a few films with softer gelatin -- Fomapan and (now discontinued) Fortepan, have a reputation for scratching easily, but again, most of the opportunities for damage occur before fixing.
Generally, you'll get best results on both film and paper with a modern rapid fixer. There are arguments to be made on alkaline vs. neutral vs. acidic fixers, but generally, that makes little to no difference, as well. Where rapid fixer gains over older types is that it not only works much faster, it has much greater capacity (you're less likely to underfix due to exhaustion) and that goes double for films with high iodide content, like tabular grain types (T-Max, Delta, etc.).