I’d read that Kyle preferred the .338 Lapua. At least that’s what I remember from his book.
True he used both during his tours. Not sure about when he used either; there seems to be some confusion regarding the timing. Some of the images claim he is holding his CO’s “300 Win Mag” some claim, including in his book(as I recall), a 338. I think it most likely was the weapons evolved and he changed as one grew on him. I guess a 338 would be like a mud truck and a 50 would still be the monster truck.