Id say tires then shocks... but its most likely a combination of the two.
The 5100 is a digressive shock (starts off stiffer), that is a bit stiffer than some, but not by a large margin. That said, I do like that particular damper.
The added weight of the tire can influence what you feel since you have more mass on that shock which can at times feel like chatter or a bit more jarring depending on the terrain. Less is absorbed into the tire and becomes the shocks problem to deal with.
Personally I am a fan of a SL, C and D load ranges over E. P rated tires for a road only truck is also fine. Just depends on what you do with it...
If it were my truck, I would change the tire before the shock. Maybe you have a friends with a Toyota, I would swap rims/tires. I can feel a significant difference moving from my on-road set to my off-road set.