i was thinking the other way around, if you have a 375 then why bring a 30-06? a 375 H&H loaded with a 235gr Barnes TSX or a 250gr Barnes TTSX would be suitable for everything from impala to cape buffalo at ranges out to 300 yards. the only time a 30-06 would be better is if you plan on trying some shots over 300 yards.
the 416 is suitable for all game out to around 200 yards which is about the distance most game is shot at any way. i use a 300gr .416" TSX at 2700fps from a 416 RM and have used it on plains game with plenty of success at distances out to 150 yards (as a habit i try to get closer when possible regardless of the cartridge). the warthog in my avatar was shot at around 140 or so yards with this load (thats a 416 RM on his nose).
the only limiting factor with the 375 and 416 is the poor BC of the lighter bullets. but i dont see this as limiting enough to justify bringing a second similar gun unless you know your going to be making plenty of long shots. a better two gun combo would be something like a 375 H&H and a 458 Lott or my personal two gun combination of a Win M70 in 416 RM paired with a Heym M89 in 500 NE. the advantage of these combinations is that if something happens to your heavy rifle then you can use the medium bore rifle in its place where as if you have a 30-06 and a 375 and something happens to the 375, you cannot legally use the 30-06 in its place.
-matt