Actual brass cost is pretty much the same, but I do charge more for fireforming of the big 408 case for componant cost and labor. In the end, you will pay around $2.5 for a Lapua case and then you need to fireform it, unless its a 338 AX.
For my 338 AM, they are right around $3.50 each fully formed with correct headstamp.
Dies are around $100 more for the 408 CT based wildcats simply because the FL sizing die needs to be a 1" diameter die. You will also need a press bushing adapter which most press manufacturers make for the 1" diameter dies.
Actions are nearly identical in price. In fact if you compare a repeating Lapua receiver to a single shot 408 receiver, the 408 receiver will be less because of the cost of mag box system on the repeater. Stocks are the same, barrels are within $50 of each other.
Chambering is a bit more for the big 408 based rounds, just more time involved.
Barrel life, I would say the 408 based rounds have about 1/2 the life as the same caliber rounds based on the Lapua. No free ride for performance.....