Unless it's pouring snow or rain I don't think you'll be able to tell the difference. I think gore-tex is the only fabric that is really guaranteed to keep you dry, so it's especially nice to have some pants with it. If money isn't an issue I'd get the AK stuff.
There is for sure a difference between the two. Dry Ride as a term coined for Burton gear, every company will have a different term for it, as well as a different method of producing it. Waterproof ratings, e.g. 10,000, means it can withstand 36 ft of moisture in a 24 hour period, but the actual standards used to determine waterproof ratings used here in the U.S. is PSI.
Also, you have to take into account where you will be riding, what the conditions are usually like there, is the snow wetter or drier. And of course, even if you have gore-tex, that doesn't mean you can jump your ass in a lake and still stay dry! Also, you'll want to look for taped seams, zippers and even the material the jacket is made from, all those things play a role in determining the true waterproof ability of outerwear.
The standards for Gore-Tex are much higher and really are top of the line in terms of waterproofing and breatheability. I have the AK 3L pants and there is a significant difference (in my personal experience) between those pants for me vs. my other pants with dryride or whatever other waterproof terminology.