Going up to a 375 has some advantages, but has some disadvantages too.
Pros: Larger frontal area for more "Smack" and better SD and weights for better penetration, and bullets are common, but mostly in the heavier weights (270-300 gr)
Cons: in the H&H and other larger cases, you are going to be burning more powder and getting more recoil
Unless you go with a smaller case such as the 376 Steyr. You get the benefits without the extra recoil and muzzle blast. Although your choices in ammo (235 and 270 gr loads) and brass are limited to Hornady. You do have more choices in bullets from 235 to 300 grains such as Speer, Nosler, Swift, Woodleigh, etc. From personal experience I can tell you that the 376 is a very fun cartridge to shoot and has worked very well on bison and elk with the 260gr AccuBond@ 2632 fps from a 21"barrel (full stocked rifle) that produces 1/2" groups at 100 yards.
Going down to the 338 cal also has some advantages: mostly being a larger selection of bullets and ammunition in the Win Mag version, with better performance in velocity and energy.
Cons with the Win Mag is again increased powder consumption, recoil (of which is more than the average shooter can handle well)and muzzle blast. It is a great cartridge and performs very well on moose, elk, bison and big bears. Also based on personal experience. Going smaller, one has the 375 Win and the 38-55, but both are quite a step down and are not quite so comparable. But I find the 375 Win to be a great cartridge which I thoroughly enjoy shooting and hunting with.
In lesser cartridges, you are limited mostly to the 338 Federal and 338-06; both of which have not set the world on fire, but both are very capable performers. The 338-06 is very similar to the 35 Whelen in performance, whereas the 338 Federal is comparable to the 358 Win. Only Federal loads for the 338 Federal and Weatherby was the only company to load for the 338-06. Both are fun to shoot and can be very accurate. Having fun with my 3 different rifles chambered to the Federal and my custom 338-06.
Some have preferences to either one of the 3 calibers; I find them all to be interesting, fun to shoot and hunt with and having their own virtues (but this may have more to do with the rifles that I have them chambered in).
Another cartridge that is in the same league as the 35 Whelen, 338-06 and 376 Steyr, but not mentioned yet, is the 9.3x62. It does have the advantage of shooting heavier bullets from 250-300 grains, and has gained a very strong reputation in Africa on dangerous game, where it has been called the "30-06 of African cartridges". Just starting to play with this cartridge, but have been wanting one for quite some time. Had to wait to get a left handed to Sako, before I pulled the trigger, both figuratively and physically!
At this time I have rifles in the 338 Federal, 338-06, 35 Rem, 356 Win, 358 Win, 9.3x62, 375 Win and 376 Steyr. And I like them all! LOL
I know several people who have Whelens, and they all love it. Perhaps you should try another cartridge, either bigger or smaller, or both (I know, I am such an enabler! LOL), but hang on to your Whelen so that you can make your own decision on which to keep and use. Or you may just find you like them all for their own merits as I do.