Depends what you're looking for from the experience.
My favourite full-on experience of the last couple of years was Legend of the Five Rings, though the game is now old enough that its prohibitively expensive to catch up. Fantasy Flight Game's Living Card Games are always best enjoyed by getting in when they start up, rather than a year or two in. FFG generally makes great card games, and I've had a whale of a time with A Game of Thrones, and Warhammer Invasion, and W40K Conquest. However, after a while they become unprofitable because it's hard for new players to buy in, and the games collapse, and you have to start again with a new game. If your love life is a string of 1-year relationships with folk who you were sure were "the one", then FFG LCGs are for you.
Keyforge is occupying a lot of my time right now, as it's a lovely quick and casual game that has a low financial investment to buy into, but still has a lot of reward for skilful play. It's also by Richard Garfield, the guy who created magic, and has all the pros and cons of that. That is to say, the pros are that its a well-balanced and accessible game with a good understanding of what makes card games great, and has it's own clever unique mechanics. The cons are that Garfield's real talent is making games that you'll look back on three years down the line and realise you've spent a small fortune on. Keyforge is super-accessible and easy to start playing, but if you want to get serious, you have to buy and buy and buy to get the perfect deck.
Historically my favourite game was Vampire: The Eternal Struggle, but that was more about it being designed as a 5-player experience. Indeed, it was TERRIBLE for duelling with. The game being built for big groups made it an excellent place to demonstrate tabletalk skills, and for the player with the best strategic awareness to win, rather than being all about what was in your deck.
I have a lot of fondness for the old Babylon 5 CCG. Their set distributions were for shite (the initial set was 400 cards, 100 commons, 100 uncommons, 200 rares!), but gameplay itself, even with the starter decks, was excellent. Players would take the role of Ambassadors to the Babylon 5 council (or, with expansions, the "home government", so you could have a President Clark player and an Ambassador Sheridan player) and try to build influence for their faction, manage inter-faction tensions, commit intrigues and assassinations, and even start the Shadow War. The Vorlons and Shadows were not playable as separate factions but you could build your deck to morph into "Shadow-Influenced Centauri", or "Vorlon-Influenced Psi Corps", etc.