The three you listed are virtually identical. Not enough seperation to make a call based on ballistics alone. Consider other factors to base your decision on. There are many differences but ballistics are not one of them. From all the rifles I built and all the other rifles guys brought to my range that I chronographed, the averages would be like this. The 338-300 ultra is slightly faster than the 338 ultra. Then the 338 lapua is slightly faster than the 338-300 ultramag. Probably because the lapua brass allowed the lapua to be loaded at higher pressures giving it a slight advantage. This is considering highest velocity loads. However the accuracy loads of these three cartridges all fit in a 150 fps (2725-2875)range pretty much and most within 100fps (2750-2850). Either of the three can fit anywhere in that 150 fps range. In other words one guys 338 ultramag may be 100 fps faster than another's 338-300 or 338 lapua with best accuracy loads, or switch them any way you want. Basically with best accuracy loads they are identical because they all fit within that specific range. All are equally extremely accurate.
So with that one has to consider other factors that are important to him. Ease of reloading and if you have a standard magnum action to rebarrel. And if that action happens to be a mk5 wby which is a huge plus and makes all the difference allowing you to go to a bigger 338. Basically if you have a standard magnum action that is not a wby mk5 the choice would be one of the ultramags that also would be much cheaper to reload. The standard 338 ultramag is over the counter products with no resizing cases or fireforming brass making it easier and cheaper still. That is why I stopped building the 338-300 ultramag in 2001. If you have a mk5 wby action or you are doing a custom action rig then the choice would be the 338 lapua improved, 338-378 wby or one of the improved versions of the 378 case or 416 rigby case. These would step you up considerably in performance over the ultramag case and all are equally accurate if done by a top gunsmith who is familiar with doing the chambering you decide on. Velocity performance is critical in long range shooting because of the unknown variable which is wind. You want to eliminate as much of that as possible and the higher velocity chamberings leave less of the unknown to figure.