I have chambered rifles in both cartridges for customers and would lean towards the 338 Lapua version.
The Improved version rifle utilized a 35 degree shoulder and tight neck requiring turning case necks. The rifle was intended to be a 1500/2000 yard varmint rifle utilizing 1000 yard BR technology. The reloading dies required a special sizing reamer for FL sizing and sending the Newlon die blank off for nitriding. Neck and seating dies were done with the chamber reamer. The rifle is superbly accurate, but the total cost of dies was prohibitive for most purposes.
The Lapua Mag rifle was a rebarrel of a Sako TRG and intended for long range plinking. The reamer was tightened up in some dimensions, but uses standard loading dies. The customer sent me a picture of a him holding the rifle and standing by a 1200 yard swinger that had a fist sized 5 shot group on it. The barrel on this rifle was a Hart slightly heavier than stock and was put on mainly to solve a fouling problem with the factory chrome moly barrel. Depending on the conditions, I would consider this rifle to be a legitimate 1000 yard elk rifle.