The Savage 110 comes in 375 Ruger and depending on whether the "Brush Gun" or the "Bear Hunter" is chosen they can be had from about $800 to $1200 MSRP. Of course one may find them cheaper at various gun stores and gun sites.
The 110 is a push feed rifle so you may or may not want to consider that depending on you religion regarding push feed vs. controlled round feed. The 110 action is a time proven, accurate action, that is very strong. However many people are put off by their use of sheet metal mag boxes and the aesthetics of the rear of the bolt.
One thing about the 110 is there are many aftermarket upgrades such as pre-fit wood stocks to change the appearance, if that is your desire.
Also if a decent used 110 chambered in common mag calibers can be had at a good price, the 110 barrel can be easily changed and the headspace.
Headspace can be set on a 110 by just about anyone with a min. of tools, and very limited mechanical skills. So many existing 110's with common magnum chamberings can be rebarreled to the 375 Ruger with a min of work and expense. Models after the '90's can be easily converted to 375 H&H. The 375 H&H will require a mag box change and some slight stock work on the mag box area, unless it is an Ultra Mag chambering.
For me the 110 is a true nuts and bolts field gun, that can be improved greatly with simple glass bedding and an upgraded trigger.
The 375 Ruger will do anything the 375 H&H will do and vice versa. However the 375 H&H ammo is available anywhere in the world. At this time that can't be said for the Ruger.