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So .308 Winchester and 7.62x51 NATO are essentially the same cartridge. The main difference is .308 Winchester is the commercial version of 7.62x51 NATO and has a slightly higher pressure. So yes, if your Sig Cross is chambered in .308 you can shoot this Winchester Service Grade 7.62x51mm NATO 175 Grain Ammo through it.
M118 LR is loaded to an overall length of 2.830”; +0.030” longer than standard .308 Winchester/7.62x51 ammo, so it may not fit in some magazines. MagPul does make 25rd. magazines specifically designed for the M118 LR load, however they may not fit all rifles, and also may not drop free when the magazine release button is depressed, so you may need to pull the magazine to remove it from your weapon.