These are games that are meant for people with a little bit more experience. They have more rules than other games, tend to take longer to play but tend to offer more customization be it through expansions or many different strategies and ways to win.
Pathfinder Adventure Card Game The gameplay in Pathfinder ACG revolves around 2 key mechanics, Exploring and Checks. Even though they go hand in hand, to properly understand Exploring it is important that you understand how Checks work. Your goal is to defeat the Villain before the blessing deck runs out or your entire party is dead. In order to defeat the Villain he must have no Location left to escape to.
Warhammer Invasion - Limiting a game to only two players already starts to limit its accessibility but make that a cuthroat destroy your opponent game with many tactical decisions to be made and you really aren't left with anyone to play other than experienced gamers. Warhammer Invasions is an awesome 1v1 conflict game, highly recommend it if you are in anyway interested, give it a chance and a play through.
A Game of Thrones: The Card Game - Although some rules are more complex than others, most rules can be learned with just a few minutes with a good explanation. Teaching someone politics, cunning, diplomacy and strategic timing can be a little harder. A two player Game of Thrones LCG is boring to me, I'd rather play Warhammer, however with 3 or 4 players the gameplay takes a drastic turn and gets far more interesting. One of my favourite 4 player games.
Space Station - Although the rules are basic and its a short card game that almost looks like it can take on the role of your next filler, its not. Space Station is an intense game of expansion, although there is a fairly large luck factor, this can be drastically minimized by careful construction of your space station. I found it took 5 or 6 plays to really "get" the construction which is very well executed mechanically, although I rarely ever win I do enjoy playing space station.
Call of Cthulhu - Mechanically speaking CoC is very interesting, if you are interested in the deck building aspect you are in for a treat, the CoC LCG has a long list of expansions and chapter packs all adding more fantastic cards, the artwork is superb, the lovecraft theme is amazing and includes many horrors, icons, and classic references. Playing CoC is elegant and the game play flows so well, all that aside, my favourite thing about CoC are the Cthulhu statues used by both players.
Dominion - Closer to medium than heavy, Dominion is a game that really allows you room to adjust the difficulty. By giving you a wide variety of cards to choose from and multiple ways to choose them time you play feels slightly different. If there is a game that is a shining example of how smooth game play should be, Dominion is that game, its no wonder Dominion took the hobby by storm and lead to the release of dozens of very similar "deckbuilding games".
Tikal - The oldest game in my collection and definitely has gotten me more bang for my buck than any other game I own, Tikal is a strategic worker placement game, every turn you are given 10 activation points and it is up to you how to spend them, moving through the jungle, digging for artifacts or transporting more workers into your camps are only a few of the ways to spend those points, although there is a semi random tile draw mechanic and you reveal/build the board as you go, Tikal still feels incredibly sandbox and allows room for a lot more strategizing than most board games do, instead of picking one of a couple paths, you can really create your own path in Tikal.
Caylus - When I think of the "hardest" game I own, Caylus comes to mind, not because I find it hard, in fact I think casuals should be able to pick it up as long as they have played a worker placement before. Yet everyone I show to, regardless of my explanation technique finds the game simply overwhelming. There are some tricky mechanics namely the provost and the bailiff but really they are pretty easy to understand after the first couple rounds. Caylus gives you multiple routes to victory, probably more than most games I have played, it really is one of the best worker placement games to date, hard to find a copy and I would recommend learning from someone as the rulebook is not very good at all.
Rune Age - Multiple games in one makes it easy to tailor your experience to your gaming group, personally I like the cooperative vs the monster deck my only issue is one of the cards is way too powerful and always makes us fall behind, thats okay though, I like a challenge. My only issue with Rune Age is the lack of card choices, and the factions you have to choose from are not balanced for every game mode. Still you can learn how to play a deck building game in a way that more suits your play style and is more exciting to play with armies, weapons and monsters than it is villages and townsfolk.
Kairo - Although the box's suggested age and artwork, Kairo is not a super fantastic kids/family game. It is an abstract strategy game, very sandbox like and with lots of player interaction. Kairo is DEEP, and unfortunately the components art/colour scheme make the board a bit of a visual clusterf**k. Games where you play a symbol and not a colour always throw me off at first, if you have been playing a lot more mainstream games this can be difficult to adjust too, even with my glasses and knowing how to play sometimes staring at the board can give you wtf moment and make your head hurt. This is the game in my collection that I wish hit my table more, to put it simply, Kairo is not for everyone and I really wish I had someone to play with.
Rex: Rex is definitely towards the heaviest end of the spectrum, play time taking between 2 and 3 hours. There are seemingly infinite strategies in Rex, you will choose between 1 of 6 races each with variable powers and fight for control of a continent sized city, Mecatol Rex. This is a game where you end up "playing your opponents" more than the actual game, lots of backstabbing, negotiation, bluffing, bidding, combat and backstabbing.
Android Netrunner - Is Netrunner all its cracked up to be, I mean how has it locked down the hotness section on Board Game Geek since its release basically never losing a top 3 position? Well I am here to help you make that decision for yourself. First I will give a brief overview of how the game is played, then I will compare it to the other LCGs I have played.