In my experience, my family's hondas have been more reliable than our toyotas. I'll give a short reliability comparison of our 2010 corolla gli with 215k kms and our civic 2013 manual oriel with 225k kms. Corolla's suspension was gone by 140k kms and it was rarely taken outside lahore. Civic's suspension started giving problems after 210k kms and it was regularly taken out of lahore in village areas. Civic's suspension issue is also only just noise, rides perfectly, while the corolla has ride problems. Corolla needed a clutch change at 140k kms and is due for another clutch change now, civic is still on original clutch working well, and trust me, civic's clutch has been abused a lot more. Corolla has needed oxygen, camshaft and crankshaft sensor changes while civic has needed none. Corolla consumes around 500ml oil every 2k kms while civic doesn't consume a drop of oil. Corolla has tons of creaks and rattles everywhere, while the civic has just one rattle in the roof. Corolla has needed change of 2 engine mounts, civic has needed none. Loads of other issues with the corolla like electric windows, starting issues, etc.
So yeah, toyota being way more reliable is only a desi belief that is well propagated here. Throughout the world, toyota and honda are considered to be on equal footing in terms of reliability for econoboxes, the actual super reliable toyotas are the cars that honda barely competes with, like land cruisers, tundras, hiluxes, etc.