I suspect there will be more complicated card games than bridge but none of them are widely played. The main era for card games (based on a standard deck) is over since many more games and entertainments are available. Game makers also don't make any money inventing new games based on a standard 52 card deck, which is probably why there are a great number of little boxed games sold with cards in 5 suits or running from -10 to 10, when in fact the same game could be played with a basic pack of cards and amended rules.
Bridge is much more complicated than solo, whist, hearts, spades, all the rummy variants, solitaires, bezique, poker, and anything else I can think of. The bidding for the contract is complicated as you have the levels of contract, variable suits and no trumps, doubles and redoubles, and limited bidding space. That's just for 'natural bidding' and the bidding systems make it more complicated still. Card play also requires a lot of skill and can hinge on information gained in the bidding. There are also opportunities for bluff, sacrifice, misdirection, gambles, and many other competitive plays. An understanding between partners is also needed. Duplicate bridge provides tournament scoring for this game even with random initial deals.