The higher load rating will be able to resist overheating at higher loads than required. This inevitably creates a stiffer sidewall and with that, a firmer ride.
However, higher rated tyres tend to be used on heavier vehicles at higher pressures. Used on a lighter vehicle, at lower pressures it's unlikely to make much of a difference and if it does, I've yet to see an exact figure. What I mean by that is that a tyre designed to carry 10% more load won't feel 10% firmer.
Going to a higher rated tyre will give you many more options. If you go for a larger tyre, something like a 235/65/17 for example, you can run them at slightly lower pressure than the standard sizes. This would probably cancel out any perceived increase in stiffness from a higher load rating.