With the right loads the .375 H&H will match the trajectory of the .30-06, and does it with a much heavier bullet.
Both are fine rounds, the .45-70 is going to be a little cheaper, and more common.
Bullet selection is greater for the .45-70, with a fair number of jacketed and wide variety of cast slugs available. The .375 has 3 basic bullet weights common, and only two of them are currently factory loaded.
I've been shooting various .45-70s going on 30 years, only got a .375H&H last year. For fun shooting, I'd pick the .45-70. If you want to get serious power, either will do, from the right rifle. The .375 is way easier to hit with at extended ranges.