I own and like both very much. However if I had to choose I'd take the Adamas over the Vulcan in a big way.
Having said that. The Vulcan is a great knife. It's a strong, smooth, tough well made knife. The 3.5" x 160" VG-10 blade at 59-60 HRC is a good steel that takes a great edge. It's my favorite Sog folder hands down. You can't go wrong owning one but compared side by side with the Adamas I think the Adamas superior in all areas and on all levels.
The Adamas 3.82" x 160" D2 steel blade at 60-62HRC is a far better steel in the areas of edge retention and toughness. You may find it more difficult to sharpen though. It's slightly less corrosion resistant but not significantly enough to make much if any difference to me. In the area of edge retention though, it's a much better steel.
In the area of pure strength, the beefed up AXIS lock, stop pin, and liners out matches the Sog's Arc lock. No question there.
They both feel good in hand so that's subjective and personal preference. The Adamas is a bigger heavier knife though, 7.70 oz vs. 5oz, so as long as size and weight isn't a factor then I'd take the superior strength and steel of the Adamas over the Sog.
Not sure where your looking to buy but I suggest you look around. You can get the Adamas as low as $125 - $135 shipped depending.
So, like I said. I really like both, would be happy with either, but if given a choice and could only have one I'd choose the Adamas.
Best of luck!