Loosened side vs fixed side can make a difference on bottom brackets but not on hubs. The axles are completely side indifferent so don't sweat it.
As for grease, I use synthetic grease these days but IMO the major factor in bike hub grease is cleanliness and the ability to withstand the inevitable contamination by dust and moisture that will get by the seals. Periodic cleaning and re-greasing is the best defense here.