Lapua is the Company in Finland that designed the rounds, Im assuming your talking about the .338 lapua used in tactical rifles for long range precision shooting rifles like the Accuracy international and Sako brand rifles (the 2 most prominent .338 rilfes i would say).
the .338 is based off of a .416 Rigby which was necked down for a .338 inc bullet hence the name, Best example would be like a .22-250 or .243 which is a .22 bullet or .243 bullet on the case of a .308, both primarly hunting rounds, the .22-250 being an excellent varmint killer, .308 is a huge overkill for something like coyote, but a .22 with enough force behind it is perfect.
There was a lot of work put into the .338 because the current main anti personnel round was the .308 which is capable of hitting things 1,000 + yards away (you can hit 1,000+ yards with a .223) however hitting a live target and a stationary target are 2 different things. From what i can gather a lot of people were using the .50 BMG, although it can take down a target fine, the round was developed for the browning machine gun not a precision rifle, however it was adapted to the rifle platform it is still not meant to be an anti personnel round.
Here are the balistics of the .50 bmg
Bullet weight/type Velocity Energy
647 gr (41.9 g) Speer 3,044 ft/s (928 m/s) 13,144 ft·lbf (17,821 J)
655 gr (42.4 g) ADI 3,029 ft/s (923 m/s) 13,350 ft·lbf (18,100 J)
700 gr (45 g) Barnes 2,978 ft/s (908 m/s) 13,971 ft·lbf (18,942 J)
750 gr (49 g) Lapua 2,618 ft/s (798 m/s) 11,419 ft·lbf (15,482 J)
800 gr (52 g) Barnes 2,895 ft/s (882 m/s) 14,895 ft·lbf (20,195 J)
And the .338 lapua
Bullet weight/type Velocity Energy
12.96 g (200.0 gr) 1,019 m/s (3,340 ft/s) 6,734 J (4,967 ft·lbf)
16.20 g (250.0 gr) 897 m/s (2,940 ft/s) 6,516 J (4,806 ft·lbf)
16.20 g (250.0 gr) 910 m/s (3,000 ft/s) 6,634 J (4,893 ft·lbf)
19.44 g (300.0 gr) 826 m/s (2,710 ft/s) 6,632 J (4,892 ft·lbf)
19.44 g (300.0 gr) 837 m/s (2,750 ft/s) 6,810 J (5,020 ft·lbf)
the .50bmg has nearly 4 times the energy as the .338, you dont need that much energy to kill a human, and the .338 delivers enough force while being much more suitable for long range precision shooting.
just the amount of material in the rounds makes them expensive, add to that the fact they they arent heavily produced for the civilan market and you get very high prices on raw ammo, and very hefty price tags on reloading materials. As mentioned before even the lower quality remington stuff can be $5-$7 per round, at the moment .338 is more expensive than .50 bmg, you can get federal .50 bmg for $2-3 a round.
