The only competitor in terms of safety record is Hawaiian, which also has a stellar history, but is an order of magnitude smaller.
But the Qantas Flight 32 is the point, this is exactly what this story is about. Confidence in an aircraft. Qantas Flight 32 was an Airbus A-380, which is exactly what you would expect to hear anytime you heard about serious accidents or plane crash; the name "Airbus". Boeing used to be the safe over engineered plane, while Airbus was a French/German/Spanish hybrid where the jokes about French cars, carried over to the planes, which led to joke slogans like this:
"Take a chance with Air France"
Boeing was synonymous with safety; but now they seem insistent on destroying their own legacy with that MAX/8 plane.
This [1] seems to disagree with you, searching for Boeing and airbus, there seem to be many more Boeing incidents than Airbus.
[1] https://en.wikipedia.org/wiki/List_of_accidents_and_incident...
Crucially, this also doesn't normalize to the quantities of planes flying. If Boeing makes up 70% of the global fleet, but only 65% of incidents, then that would mean they were safer rather than not.
Airbus has delivered more planes than Boeing in the last two years but I'm having trouble finding statistics on overall fleet makeups going back further than that.
I'm guessing that Boeing's good safety reputation had some root in reality, just like Toyota probably is a more reliable car than many other brands. Renault could be a very reliable brand now for all I know, but their reputation has already been shot, and that can be hard to recover from. Some brands really never recover, and just change their name; like LG did, GoldStar (their former name) was not associated with quality. The reason Boeing is changing the name of the MAX to 8 is similar, but a name change alone will not resurrect their image.
I'm sure at one point Boeing was a very safe plane, since I associate that brand with safety, but today perhaps Airbus is as safe (or even safer), but it's hard to shake off a reputation.