‘Simple’ is widely considered better.
‘Easy’ has more baggage.
When something is made ‘simpler’, something was changed so that, once learned, may prove ‘easier’ to a user.
Making something simpler has a cost (learning), which the user must be willing to pay. The return on investment might be that things are now ‘easier’.
When something is made ‘easier’, something was changed to reduce a cost (learning or time). Making something easier doesn’t necessarily require ‘simple’ (delegation and removal are other paths to ‘easier’).
But when things can’t be delegated away or removed entirely, ‘simple’ often comes into play.
iPhones are ‘simple’, but the 2007 release still had to come with an instruction manual (where are the buttons? What does the ‘home button’ do?) before it became ‘easy’.
Sending letters in the post is ‘easy’ because it just takes paper and a stamp. Email may have been ‘simpler’ (fewer steps, faster) but wasn’t ‘easier’ until the cost (learning) was paid.
Menus are along the top of websites because that’s where people expect them to be. Hiding them behind a menu icon on large screens may create a simpler interface, but the cost isn’t ‘worth the investment’ to visitors who are only going to be there for a few moments.
We serve people better when we remember the costs we ask them to pay, making sure that our people think that the ‘easy’ at the end of the tunnel is worth it.