H&H for sure. Short mags are all over the place and not hard to replace at all.
H&Hs are scarce and if you sell it you'll regret it for the rest of your life.
For flat shooting both shells do about the same thing with bullets of 150 165 and 180 grains. The "magic kills" I have seen from all 300s (including my H&Hs) have seemed to be best with heavy weight bullets. 200s and 220s. I own a chronograph and I do my own testing. The idea that the short mag is faster is absolutely not true. It's about the same or even a smidgen slower. Nothing at all to concern yourself over.
Taking a vote the 300 H&H wins. How about doing a search on the net for Winchester XTR rifles in 300 H&H. See what's out there. Do the same with the Super Shadow in 300 WSM. I gave $350.00 for my Super Shadow with scope .. See what the market really is. This should clarify the choice or at the minimum give more information. I prefer my Remington 721 om 300 H&H with Lyman 48 sight etc.
The OP said he was thinning his collection. He spoke of the rifles in new condition. There was no talk of cartridges or cartridge performance in his post. We are trying to make the point that the 300 H&H rifle is scarce. The Super Shadow is not. The 300 H&H is worth more money ($). Go look at the current cost of replacing each rifle. Rocket Science. Hope OP has not been run off.
Reloading and collectables: I hope OP considers the option of reloading his cartridges. Reloading is a plus on uncommon cartridges. I'm not wiling to allow my caliber choice to be dictated by Box Box ammo offerings. My 300 H&H is a Remington 721. Yes, I load for it. Yes, it's way more economical. Glad to hear he is keeping his collectable rifle' Seems like some folks did not understand collectible.