I think toyota beats honda in quality. If you go here:
https://www.carcomplaints.com/Honda/Accord/ you can see that when you compare cars with similar sales volume like the accord and camry at least the last 5 or 6 years toyota has won.
We studied the Toyota quality system in my business classes. They put a lot of emphasis on quality. They use the teachings of Edward Demings (https://en.wikipedia.org/wiki/W._Edwards_Deming).