Oil finishes - can give you a great look on a gunstock ...
But pure oil finishes - will repel water - but they aren't waterproof --and over time, you may find the finish gets a little "muddy" ...if sustained water exposure to the stock from ( rain, snow, etc ) gets thru the finish into the wood.
Varnishes - like Watco Danish Oil, urethanes, verathanes etc - dry harder, and build one coat on top of the other - and give you a harder finish than anything you can get from a pure oil finish. Not all varnish finishes have to be shiny ...you can get a matte finish if you want it ...or semi-gloss or whatever ... Varnish - will give you a lot better durability against weather ...
But it depends on how you use the gun / how you want to protect it. Oil finishes are much easier to maintain ....and even if the stock gets muddy .... you can sand the stock / put another coat of oil on it ...to bring the "oiled" look back to it.
Most Linseed finishes - are polymerized linseed oil - not pure linseed oil - so they're a hybrid. There is so much "marketing speak" in finishes ...its sometimes hard to tell what you put on a gun .....
http://www.brownells.com/.aspx/pid=5531/Product/PRO_CUSTOM_OIL_GUNSTOCK_FINISH
This product is really a varnish --- it has oil in it too / but the urethanes make it a varnish / it dries hard and will build with each successive coat. True oil finishes - do not build - as you add another coat ( wax is the same ) - each successive coat, just melts the wax beneath it ... so you can put 9 coats of wax on something / but its really just one coat of wax - it does not build....
Not all gunstock finishes contain linseed oil ...
I've had Browning Citori shotguns / with oil finishes out of the factory - that held up pretty well for about 3 years ( like the Citori 525 or 625 series ) - and then the finish got muddy looking. I removed the oil / sanded the stock - and put this Pro Custom gunstock finish on them ...and they were much better protected longterm. But it depends on what you want ...
There is no right or wrong finish ...