Sticking with conservative published data on Hodgdon.com and using Hornady's ballistic calculator for 338 LM vs 7mm RUM you have:
1153 fps @ 1700 yds 92 gr Retumbo BC=.659 for Berger 7mm VLD 180 gr (max load)
1022 fps @ 2000 yds
1130 fps @ 1700 yds 98 gr Retumbo BC=.682 for 250 gr Berger Match Elite Hunter
1011 fps @ 2000 yds
1157 fps @ 1800 yds 94 gr Retumbo BC=.818 for 300 gr Berger Match Elite Hunter
1078 fps @ 2000 yds
For 59 deg F @ Sea level.
I'm told the 7mm will eat up barrels but the cost of shooting the 7mm is 50% that of the 338.
1153 fps @ 1700 yds 92 gr Retumbo BC=.659 for Berger 7mm VLD 180 gr (max load)
1022 fps @ 2000 yds
1130 fps @ 1700 yds 98 gr Retumbo BC=.682 for 250 gr Berger Match Elite Hunter
1011 fps @ 2000 yds
1157 fps @ 1800 yds 94 gr Retumbo BC=.818 for 300 gr Berger Match Elite Hunter
1078 fps @ 2000 yds
For 59 deg F @ Sea level.
I'm told the 7mm will eat up barrels but the cost of shooting the 7mm is 50% that of the 338.