Are there any downsides to floating click lock floors versus traditional nail down floors when both are full wood?
If both are installed correctly then there isn't a ton of difference.

But the small difference - in that the floating can slightly buckle in some areas due to humidity and temp - makes nailing down the choice.  Really floating should be used if installing on slab, if you used a ton of floor leveler, or mixed surfaces.  A far as the install nailing down requires a gun but it is actually easier then glueing everything together.