For most people, their Max HR is different running than cycling.
I am not a fan of Max HR training anyhow, because it is not constant. Your given max on a given day will be affected by things like sleep, sickness, alcohol in the prior 48 hours, hydration, ambient air temp, humidity, etc., etc. LTHR% work better in my opinion because this changes slowly, down as you become more fit, up as you lose fitness. As for the zones, Andy Coggan’s LTHR zones seem to be the ones that most closely match, for me, PE.... That said I don’t train with HR, I use power meters, because unlike HR, power is instant, HR will lag behind the effort. I do track HR though because it can tell me things that power won’t in terms of my overall condition and ability to train.