My .375 wears a 1.75-6x Leupold with a heavy duplex reticle. Unfortunately, this scope is no longer made. Unless the animal is small at longer range, I wouldn’t feel handicapped with it. At some point, I may replace it with something with an illuminated reticle (Leupold or Trijicon)
I tend to prefer lower magnification ranges: 1-6x, 1.5-5x, 2-7x, 2.5-8x, unless there is a good chance, of a 250yd+ shot. Few of my rifles wear scopes with a high end over 10x and those are rifles intended for open country. IMO, you don’t want a .375 to have a low end over 2.5x.
As far as Vortex, I’ve never owned one, but have shot rifles with them. The higher end Razor and Viper have pretty good optics. However, just an observation, a fair number of these Vortex owners have had to send them in for service. These are not mounted on heavy recoiling rifles and are pretty much paper punchers. Their customer service is great, but I’d rather not have to use it.
Leupold, too, has great customer service, but in over forty years and over twenty scopes, I’ve only had to send one in for service. that was a new scope who’s power ring needed a pipe wrench to turn. I sent it in, and had it back in less than two weeks, working perfectly. I also have Zeiss, and Swarovski and never had an issue.