I haven't played LOTR, so I can't comment on that. Though friends have stated that the solo option is quite viable and enjoyable.
I do play both W:I and AGoT, both fairly extensively. They are very different games. Each has their place.
W:I games are shorter (not necessarily a bad thing) and more brutal. The tournament format is best of 3 games for each match, with 1 hour or 1 hour 20 minute rounds. Not that the tournament format matters for your purposes, but it illustrates just how quickly games can be resolved (AGoT tourney format is 1 game during an hour long round).
W:I definitely has more of a visceral feel to it, as there are LOTS of actions that straight up eliminate units or support cards without the need to enter combat. A newer player once remarked to me that everything she played just died… and I responded by stating "Welcome to Warhammer".
Both games have strong mechanics.
I often describe W:I as feeling a little bit like playing a computer RTS. You decide where to place resource generating cards (into 1 of 3 zones), to either generate money, card draw, or be able to attack the enemy (cards in the money and card draw zones can defend, but not attack).
AGoT probably has the better turn structure, as phases are shared, thus avoiding the 'advantage of going first" issue that W:I struggles with. AGoT also incorporates the inclusion of a 7 card plot deck, which is a very interesting additional to both deck building and decisions made over the course of the game.
AGoT takes 2-3 times longer, on average, to play a game (not necessarily a bad thing). It's a deeper game, with more intricate strategies and tactics. It's harder to grasp at first, as it has a LOT of moving parts. Which is to say the average game has more interactions from cards in play to keep track of. And therefore lots more opportunities for players to make mistakes and miss opportunities. Player familiarity with the game, as well as overall skill, makes more of a difference in AGoT than in W:I (note that I'm not saying W:I doesn't require any skill to play, I'm just stating my opinion that AGoT is a deeper game with many more chances for players to miss opportunities… make mistakes… during a game).
Whatever you heard about AGoT being better as a group game (i.e., more than 2 players), is misleading. The turn structure (shared phases) and multi-player rules make it a much better group game than W:I. But almost everyone I known prefers Joust (the term used for AGoT head-to-head play) over Melee (AGoT group play). Some to the extent where they really won't play Melee at all.
All in all, I think AGoT is the deeper, stronger game. However, that's not to say that W:I isn't a great game, because it is. And there are times where I simply will prefer to play W:I. Either because I want to get more games in during a shorter amount of time, or I'm simply more in the mood for W:I than I am for AGoT.
Rest assured that whichever you choose, you'd be getting into a great game. It may server you best to try to gauge the level of interest in your geographic area for each, then pick the one that is most active.