That page list every incident of any kind, including things like bird strikes and hijackings, which aren't think I would expect to affect one brand more than the other.

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.

But the person I replied to didn't talk about overall safety per mile/per plane, they talked about which company has been in the news more for accidents.

Well not 100%, I was talking about reputation. Most brands have certain attributes associated with them, for Boeing safety was one of those attributes. Just like reliability is an attribute you would associate with Toyota, but perhaps not with Renault..

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.