There are pro's & con's to both. I pesonally went with the 338 RUM as I feel it is a better fit for the 700 action. The RUM will do anything perfomance wise that the Lapua will do. The Lapua brass is REALLY bad ass & is going to last longer than the Remington brass but it is 2x the cost as well. With good prep & sorting the Rem brass has been pretty dern good.
Most of the action manufacturers that I've researched have CheyTac specific actions. Those being bigger, longer, more robust & more expensive