The 9.3x62 is definitely closer in performance to the 35 Whelen than the 375 H&H.
BUT......the difference is that like alot of US designed cartridges there is a predominance in the Whelen toward light to medium weight bullets for calibre rather than heavy bullets.
The standard load for 9.3x62 is a 286gr SP doing around 2300fps.
I have a Tikka T3 Lite Stainless 9.3x62 and it absolutely murders game.
Smaller game get full penetration and bleed out fast.
Medium game tend to drop like a stone.
I use the Speer 270gr Semi-Spitzer because it's cheap, easy to load and dropping more money on Woodleighs or other premium bullets doesn't make the game any deader.
If I was using it on water buffalo (and it's well up to the task) I'd be using bonded core ammo and solids but on soft skin game up to and including elk I reckon the Speers are ideal for it's relatively slow velocities.
Lapua brass is excellent and I've had plenty of reloads out of it.
Having said that, if your aim is to shoot longer distances and you aim to really knock down game (whilst being willing to accept some pain on your end of the power) the 375 H&H is the next step up.
The 9.3x62 is a great African cartridge and there are now 232gr bullets available for plains game but it does not have the reach the 375 H&H has at distance.
9.3x62 can mix it up with the big boys under 200yds but it begins to drop quickly at about 240yds.
And it is not the equal of 9.3x64 Brenneke.
The Brenneke is an easy match for 375 H&H but it has a larger bolt face and is much more expensive to feed, even more than the H&H.
9.3x62 is definitely a ton of fun in heavy cover or shorter ranges though.
I call my 9.3x62 "The Judge" because it passes sentence......