nb. I've changed the title from "Fails to ignore trailing slash".

I've been able to replicate it, but I don't think it is related to the slash per se, 
but rather to the fact that you've changed the minibuffer.  If I do

M-x ediff-directories RET
BKSP RET                   ; ~/ajbs/ was initialized, remove backslash
RET                        ; ~/ was initialized, accept as is
                       
I get an Ediff Session Group Panel for

*** Directory A: ~/ajbs/
*** Directory B: ~/ajbs/

In other words, I think the problem is that the default for the second directory is the 
same as the first although the minibuffer is initialized differently.  I suggest you 
get in touch with Micheal Kifer <kifer@cs.stonybrook.edu>, as it's not clear to me what 
the desirable default would be.

It also seems that ediff is comparing strings, not file system objects, to determine 
whether the directories are the same or not.  This may be a bug or an optimization :-), 
according to the user's taste.

I, Tom Browder (user name "tbrowder"), submitted this bug

I'm still haunted by the change in ediff-directories behavior
that started a year or so ago.  Now ediff-directories shows a trailing
slash in the minibuffer.  The slash seems to confuse ediff:

M-x ediff-directories<rtn>

minibuffer:  "Directory A to compare:/path/to/di1/"<rtn>
;; note the trailing slash, it didn't use to show

minibuffer:  "Directory B to compare:/path/to/"<rtn>
;; ditto

minibuffer:  "Filter through regular expression: "<rtn>

minibuffer:  <grating beep>"Directories A and B are the same:/path/to/di1/"

If I delete the trailing backslash each time, the function proceeds as
it always has (the delete '/' action on my part has become automatic
now, but it is an irritant).