ARX most likely has stronger cleaning properties and you will need to follow up with a complete fluid change after the cleaning phase (flush, not just a drain and refill).
With MaxLife ATF, you can do multiple drain and refills, get the most concentration of new fluid in but it will unlikely clean as well as ARX.
Try multiple drain and refills with MaxLife and than follow up with a fluid of your choice. Maybe it will give the effect you are looking for but most likely will be more costly due to all the fluid you will need to buy.
ATF earned it's reputation as a cleaner back when it was made of whale oil. The fatty acid esters most definitely had the ability to clean, similar in a way to the action of Auto-Rx as a cleaner, and when used in an engine short term back then, would do some cleaning. Roll forward half a century and ATF has the ability to keep transmissions clean, but the whale oil is not used in ATF anymore and it makes a poor cleaner for engines, although the reputation as an engine cleaner lives on. Maybe it could be used as a light viscosity rinse to flush out some loose stuff in an engine, but cleaning ability is nil, really.
You are better off using something designed to clean the engine or transmission. My experience is that Auto-Rx is the most effective/thorough cleaner for either, when used as directed.
Maxlife ATF or engine oil both work very well after Auto-Rx treatments are completed. I have used Maxlife this way for quite some time.