So, no one has mentioned either The Wire or The Sopranos yet?!?
In 2002 I remember starting The Sopranos, The Wire and The Shield at the same time. I only ended up finishing The Shield, and I cannot do justice to how good it is. IMHO (and in many others too), The Shield is the greatest modern television series, part of the wave that brought deeper characterization and cinematic rigor to television. It is certainly the most outwardly "entertaining" of the big three (and hence treated as less prestigious) but I truly feel that it has aged the best.
Prior to the pandemic I tried to rewatch all three series. I had wanted to introduce my wife to The Shield and she was floored by it. We then started to watch the Sopranos, but--and I hate to say it--apart from some scattered, absolutely brilliant episodes, it was awful to watch. We only lasted 3 seasons. Simply, a lot of bombast masks a lot of bad and amateurish decisions by the creators. The Christopher character is so poorly acted and lazily written (at least for the first three seasons) it was unbearable to us. I really would love to talk about it with people that watch it with fresh eyes.
We are hoping to start The Wire again soon. I'm just worried that the way the country has turned out since it ended will attenuate a lot of its potency.
Anyways, watch The Shield. It kicks ass if you love shows that kick ass but it is even better than you can imagine. The characters are all so well written (gotta love Dutch) and fabulously acted (Chiklis won Emmys year after year for this but people like CCH Pounder are just unbelievable in it.) This is the show that is the favorite of your favorite television creators. By the last few seasons the guest characters included some of the finest actors on the planet (no spoilers), which was insane if you think about the status of TV in the early 2000s.
I LOVED the ending of The Sopranos, but The Shield still has the best ending I've seen.