The difference is the 33XC can be built on almost any action a .338 Lapua can, the Cheytac needs a much larger action. The XC case is a smidge longer, but the Cheytac is a bit fatter and has 20+ more grains of case capacity. The Cheytac has the advantage as far as pure performance. I've seen a couple .408 and .375 Cheytac factory loaded options, but never seen a .338 Cheytac offering (none for the XC as well). These are best suited for loading your own. The Cheytac needs a larger press (like those capable of .50 BMG), where as I load my XC on a standard sized one (same and my .300 WinMag or .308). I would say that all things being equal, the Cheytac will be more costly and heavy as far as builds go. They can both be in a repeater action, though I thought my .375 Snipetac (Cheytac Improved) being a repeater was a waist of money.
A 37XC has the potential for larger and very high BC bullets than a .338, but as far as being better that depends on the intended purpose of the rifle. I'll say this, it takes on h@!! of a rifle/cartridge combo to beat out a .338 or .375 Allen Mag (basically an improved to the max Cheytac), especially for hunting. Run the numbers on a 300 grain .338 Berger going over 3400 fps! I've seen numbers on long barreled rifles in the 3500 fps range. I have 2 buddies that have them…amazing!