There is some interest from locals to start playing an LCG. I do not know which one we should try out though. My meta usually starts slow but then ramps up to being competitive quickly. For example a lot of us started playing L5R recently but once someone bought some sweet singles everyone had to get them. Then people started dropping out because the cost of entry became too great.

The Game of Thrones one has the most interest due to theme, but what I have read on-line suggest it has balance issues. I have played a few games of this and it was fun. Is this game better multiplayer or 1v1?

The Cuthulu one interests me more because I have not heard complaints about it due to balance issues. If we are going to play a game long term it will need to be balanced.

My question to the community is which is the better game? If we make a pack is there a certain limit to what expansions we should agree not to buy because they imbalance a game?

At the card shops in my area (Seattle), Game of Thrones has the largest scene followed by Call of Cthulhu. I personally like Game of Thrones as a game, but the barrier to entry is very high and balance is definitely an issue. For Call of Cthulhu the barrier to entry is lower (but not by a whole lot), and balance isn't really an issue overall. Certain combinations of factions are stronger or weaker than others, and most factions aren't that strong on their own, but since you mix factions with each other in any way you want it isn't as big of an issue as it is for GoT where you have to stick with a faction. I think CoC's biggest advantage is that the deck building options are limitless, so you don't have to own all the cards to make a good deck.