Which do you guys prefer and why?

AGoTv2.

Never was a big fan of Lovecraft's mythos

I haven't played Arkham Horror yet, but from what I understand, it's a solo/co-op experience where you play your deck against scenarios found in the expansion sets.

AGOT is a more traditional aggro game--not terribly dissimilar to Magic: The Gathering in that you use income to deploy resources and minions onto the board, and you go try and punch your opponent while holding back enough not to get punched too hard in return.

Personally, I think Netrunner is superior to AGOT, given that it's not symmetrical. One player is the hacker trying to build a rig that can penetrate the company's network, break the firewalls, trash the assets, steal the secret plans, while the other represents the megalithic corporation playing cards facedown to try and block, misdirect, and retaliate against the meddling hacker.

So, go with whichever game most appeals to you. Netrunner is fairly mature, AGOT is getting there but it's still kind of early days, and Arkham Horror doesn't have much more than the core set out. If you decide to go with either PvP game, just bear in mind you're under no obligation to buy the whole catalog at any pace that you're uncomfortable with. Feel free to poke around the backlog at leisure and only buy expansions that interest you. Cthulhu will be a little more regimented in what order you buy additional material, though--the monthly card packs require the corresponding Deluxe set in order to play them.

It's kind of comparing apples and oranges. I like them both. I play Arkham Horror mainly with my wife. I play A Game of Thrones with other, more competitive people. In that sense, the game I'd pick depends on who I'm playing with.

If I had a limited amount of money and had to pick one over the other, I'd pick Arkham Horror. The reason is that it's harder to find a coop game that my wife enjoys than it is to find a competitive games my other friends enjoy. The next person might have a different reason and might pick AGoT.

They're two different games that fulfill different gaming needs.

Other than the way expansions are rolled out, they're totally different. The real question here is, do you want co-op or competitive?

This is one of those ones where I default to my response of "which do you like better, chocolate or kangaroos?"

There's really no comparison at all between the games. One is essentially fully competitive, spend resources to play assets and events, MtG but better, really, the other is a cooperative RPG rendered as a card game. They're both excellent games, tho.