338 Federal is a small mid-bore. Not in the same class as the the 375s. It does best with 200 grain bullets about 2650 FPS which makes it a very efficient killer to 400 yards without much recoil. I have one. I like it. I will use it on a Nilgai cow whenever I go but I might take the 350 Rem Mag or 9.3x62 for a bull.

.338 Federal is a sleeper. Read about it, great cartridge.

Get one in a Cooper Rifle

Nilgai are not plated in armor.. 30-06, 270 , 7mag, and all the short-mag cals are wayyyyyy big enough........ I wouldn't hesitate folding one up with a 308, I'd laugh at the outfitter then go book a hunt with someone else.....

If you think you might want a larger diameter bullet, look into the 338 Win Mag. Its considered great elk medicine and I would say that Nilgai and Elk are similar in size. Most of the outfitters I have corresponded with say that 300 Win Mag is minimum for nilgai, and you have that covered with the 300 WSM. Just use a good bullet and put it where it counts.