My suggestion would simply be to try different guns before you buy. If you are fortunate to have an active local gun club with trap and / or skeet shooting facilities, show up on club shoot day(s), meet other shooters, and most people won't mind letting you try their gun. My experience is most shooters are only too happy to help each other at the range, talk guns, and help each other.
The only anti-semi-auto bias you would get from serious trap / skeet shooters is that the semi auto's eject cartridges all over hells half acre, and it is annoying. But your purpose is hunting, and that is not a concern.
As you mentioned, you have been hunting for many, many years... and to that point, hunters have survived just fine without the technology in today's semi-auto shotguns. Less recoil is the major gain, like the others here posted.
Personally, I chose not to go with a semi-auto... Most of my shooting is clay shooting when I'm fortunate to have some time... and I shoot cheap trap loads. Owners of semi-auto's warned me that semi-auto shotguns tend not to shoot cheaper shotgun loads well at all. They explained that the cheaper metal at the base of the shell and plastic shell itself both expand more in cheap loads, which tend to cause semi-auto shotguns to jam. Thus, a semi-auto was not for me.
I have a Benelli SuperNova Pump which can handle Magnum shells, reliable, and affordable. I have a well made, and affordable 28" CZ Canvasback over/under 12 gauge on order... that will be a great field gun and though maybe 2 inches beyond ideal, a fine skeet shooting choice too.
Another shotgun that will take much longer to arrive is a rather pretty Browning BT-99 34" Golden Clays gun that will only be shot for trap shooting. It is expensive, sure, due to the grade 5/6 Walnut & some other cosmetic reasons... the adjustable comb and stock , sure, has utility too... but it was something special I wanted... a gun of my dreams I have worked hard for, will use the most...
But you know, no matter how well I end up shooting it (the pretty BT-99)... an old, well looked after Winchester Model 12 my father gave me... with none of the fancy choke tube technology... just a simple full choke barrel... I'll consider myself lucky if I shoot anything better than I shoot that lovely Model 12.
