It's a tough call between my .30/06 and my .375 because I like both and could probably get by with either as my only rifle for the rest of my life. Both are Brnos, the .375 is a custom 602 chambered for the .375 Ultra and the '06 is slightly tweaked factory ZG-47.
The .375 is a shorter thus better heavy cover gun, although that issue could be resolved at anytime by my gunsmith if I chose a .30/06 carbine.
At this time in my life, I need a dedicated gun for bear work; and the .375 has a decided edge over the '06. Not that the '06 won't kill any bear on the planet, but there is a difference between a hunting rifle and a protection rifle. However I hasten to add, that should the .375 be loaded with a light for caliber bullet and the '06 with a heavy for caliber bullet, the advantage of the .375 maybe less apparent than one would at first think. I have had the luxury of a small supply of wonderful 380 gr Rhinos for the .375, but should I be restricted to a 260 or a 270 gr bullet, the .30/06 loaded with 240 gr Woodleighs though not the equal, becomes much closer in performance.
Trajectory is similar between both rounds, so that's a wash. I can shoot cast bullets with good accuracy in both rifles for my small game shooting needs. When loaded with full powered ammo, both cartridges are suitable for use on any North American big game over 100 pounds. The '06 has an edge as a varmint rifle due to the light weight bullets available for it, (the Speer 130 gr HP has proven accurate and deadly) but I'm not much of a varminter or a pelt hunter these days.
For practice shooting with full powered ammo the '06 is cheaper and less fatiguing, but with cast the cost is similar and either can be shot with little fatigue.
In the unlikely event that I was to go on another big dollar big game hunt, I would opt to carry the .375. Such a hunt would involve dangerous game, either as the quarry or as an interesting diversion while hunting lesser game and the .375 is a sensible minimum caliber choice for hunting in such environments.
I guess then I've answered the question from the standpoint of my current life style. The .375 is the correct answer for me, provided that I can continue to get the components I currently enjoy. Should we get to the point in this country that we are allowed but a single centerfire rifle, we could certainly expect severe restrictions on handloading and component availability. A few years ago I was not restricted to the number of handguns or to the type of handgun I could have on my ATC. Today, under what is our best bet as a gun tolerant government, I find myself restricted to 2, neither or which can now be an automatic. Things aren't likely to get better, and such a question as being restricted to a single centerfire rifle might have to be seriously considered in the future.