Masuda Method is better than Murder Method, for three specific reasons.
One, you have the 1/512 immediately, assuming you have the Shiny Charm, as opposed to Murder Method's max odds after many, many KOs.
Two, it's more productive to keep churning out Eevees with Flame Body and the Oval Charm, as it's far more consistent and not based on luck like it can be in the wild.
Three, there's a glitch with Murder Method, making it so it doesn't always give you the boosted odds. I believe there's a 3% chance of getting the better odds? An utter waste of time.
Hope I helped, and good luck with your hunt!