Sure! In terms of deckbuilding, in AGoT you are mostly limited to the house that you play. This is a sort of "macro-level" restriction which means that your effective cardpool when building a deck for any particular house is more or less one-sixth the overall cardpool. In CoC, there are no such "macro" restrictions which means that your effective card pool is...the entire cardpool. Most players tend to limit their decks to two factions, but it is possible to do 3 or more faction decks. Every time I go through the card pool on the search engine or just read through my cards, I discover new and interesting interactions between cards from different factions. In my opinion, this takes a lot of the emphasis off of what AGoTers call "Jamie" style deckbuilding, since the inherent nature of deckbuilding in CoC stresses card interactions. There are almost 100 different faction combinations you could do, with a myriad different card permutations within each combination.
In terms of tactical decisions, I feel that the three different challenge types (not to mention the dominance phase) is what makes AGoT shine as a game. AGoT allows you to pick and choose which challenges you want to let through; but since the board changes dramatically from round to round, it's much more about making the most of each individual challenges phase to maintain absolute card advantage. CoC has this is a slightly different but equally engaging form. Each time you commit to a story you have to think about how you will mitigate the effects of the 4 struggles, but all at once, and you're not safe from "claim" of struggles as the attacker. Simultaneously, you have to think a step ahead for your opponent's next turn. AGoT is a little more forgiving for power, so you see a lot of people leaving challenges unopposed in order to swing back to get power when they attack, but in CoC the stories act as threshholds - it's as if once you get to 5 power, you can't go below 5 power. This is what makes stories more critical in CoC than any individual challenge in AGoT, but also why CoC games tend to be faster. This gives the story phase in CoC a lot of pressure, and requires you to constantly think about maintaining enough board position to not fall too far behind.
I am a little hesitant to over simplify it, but think about the mechanical differences between AGoT and CoC. AGoT has a draw cap, relatively easy-obtained resources, a random discard mechanic, and ubiquitous reset mechanisms. CoC has no draw cap, relatively limited but scaling resources, and no real ubiquitous resets. This translates to me that AGoT is about absolute card advantage, while CoC is about relative board advantage. It's a slightly different way to think about approaching deckbuilding and playing the game.
(Sorry, I'm probably rambling a little since this is the first time I've tried to write out my thoughts on this subject.)
Wow, thank you for that, Danigral. Like Toqtamish I've been flirting with the idea of giving CoC a swing (though I'm in the process of a move for the next month and a half or so, so I probably wouldn't take the plunge until August at the earliest). As primarily an AGOT player, that was a great read that did a fantastic job laying out the similarities and key differences between the games. I've played most of the LCGs at this point, though Star Wars is the only other one I've kept up with. Once I'm settled after the move, I'll definitely go about finding a local CoC playgroup and see what I think of this game.