Hello redassnavajo,
Ejectors are my preference but, only slightly.
In other words, at my blue collar pay level, twice I have found an otherwise "excellent in every other way" double, (especially including a reasonable price) with only extractors but each time, I bought them anyway, trained mightily with same, and happily hunted with them (each a few years apart).
If you "use enough gun" as Robert Ruark had once said "and you shoot it well in the first place", (as I had once said - LOL), ejectors vs extractors becomes nearly pointless, except perhaps as DUGGABOY1 pointed out - among an angry mob of elephant (I however am too dull to have ever worried about it .... at least not very much).
Also, I totally agree with DUGABOY1, in that I see no earthly use for an "automatic safety catch" on any hunting rifle, double or otherwise.
So far, I have hunted with the two separate double rifles mentioned above, in Africa.
Once was for "plains game" and once for buffalo and "PG", both as mentioned were extractor types only but now, those have been sold and my double rifle today is an ejector gun (that sadly I've not bagged anything except targets with).
Cal Pappas (fellow AH member and world authority on double rifles) has hunted many times in Africa with vintage English doubles, I believe most of which are extractor guns only.
I have not heard him complain that he wanted ejectors on any of his many African (and Australian, North American, etc.) adventures.
Extractors or ejectors, either way - for big game hunting, from bayonet range out to about 150 paces, there is nothing quite like a double.
Cheers,
Velo Dog.