Breaking Bad isn't an HBO show. So I assume we're just asking, "has Netflix produced any world-class content". The answer to that is yes.
The jewel in their crown, their "Game of Thrones", is clearly Stranger Things. It's undeniably successful, each new season a cultural event. I'd put Stranger Things up against any HBO show for relevance and impact. (Perhaps not for artistic excellence; but, The Wire is the best show that's ever been on television, and it's far from the most watched).
Add to that Black Mirror, Bojack Horseman, Sex Ed, the annual Flanagan miniseries (Hill House, Bly Manor, Midnight Mass), Master of None, and Big Mouth.
They're doing about as well as any premium cable channel ever has. Doesn't, of course, mean you like their content! But I have about as much faith in Netflix coming up with a new prestige show than I do in HBO, most of whose recent stuff has left me pretty cold.
Honestly, Game of Thrones notwithstanding, I'm not sure that there's a lot on HBO I consider must see level content either although some is quite good.
I'd probably consider them about a wash for content.
Considering they have a lot more flexibility than your average network, I’m surprised Netflix hasn’t made movies or mini-seasons to wrap up stories more common. That would be a huge improvement over what they’ve done with a lot of their original content that didn’t quite make the cut.
Game of Thrones had far more consistent cultural impact across all seasons (although they managed to nuke its legacy completely with the horrible last season).
(I also have no knowledge or interest in LoL.)
Another thing that's easy to sleep on is that Netflix is much, much better connected to its audience than HBO is to its own. Netflix makes a lot of content that I couldn't be less interested in, but that's probably a strong positive indicator for them; I obsess over The Wire, Deadwood, and Community, and am thus pretty clearly a niche audience. For years, HBO did a good job of serving people like me, to their detriment.
Tiger King & Squid Game were both pretty impactful.
Have they? Have they really? As far as I can tell, nothing that Netflix has ever done in-house has ever come close to the best of the cable channels. Like, The Witcher is fine, but Game of Thrones it is not, neither in quality nor buzz/cultural significance. House of Cards is no Succession and Ozark is no Breaking Bad. Nothing they have could even come close to comparing to stuff like The Sopranos or The Wire in terms of cultural impact. The closest they've ever come, in my opinion, is probably with Making a Murderer, and they've spent the last couple of years churning out pale imitations that make Netflix look like "True Crime TV".
You're paraphrasing that quote from the Netflix CEO that goes like "We want to become HBO faster than HBO can become us". To me, HBO has won that race handily.