So what is the difference between Basic, B/X and BECMI?

[aramis erak]

And BX is also available in the form of the critically-acclaimed "Old-School Essentials" retroclone.

Having read it, no, it's not.
The inclusion of ability checks as core (OSE), rather than optional (X51), change to undead turning by HD instead of by named type, and a number of other minor changes make it not quite the same. Comparable to jumping from BX to Cyclopedia...
Not that they are bad changes, but they are changes.