Capacity wise, the 7mm-338 Lapua has nearly identical case capacity to the 7mm RUM, within a grain or two in capacity. IF your going to stay with this class of capacity, you probably would be better with the RUM in a factory receiver.
Yes, the 7mm Lapua could be loaded to higher chamber pressure but the advantage would not be all that great over the RUM.
My AM is a dramatic change in the Lapua case. shoulder location is moved forward roughly 50 thou, shoulder angle sharpened and body taper set at min. Case capacity is easily 10% over the RUM or 7mm Lapua.
With any of these, your best served with heavy bullets. 160 is what I recommend as minimum to get these large capacity cases working consistantly. Heavier is even better. 180 grs are great, I have heard the 189 Caut bullets are very good also. The 200 gr ULD RBBT is the best I have used in my AM but only with the very slowest surplus ball powders.