> I expected to get the same results for these two \showbox commands.

Yes you should.

Consider the following (as long as the 8bit lines of latin-1 get
through the mail)

It produces four identical results, each looking like:
> \box0=
.\T1/cmr/m/n/10 ^^c1
.\T1/cmr/m/n/10 ^^dd
.\T1/cmr/m/n/10 ^^c1
.\T1/cmr/m/n/10 V


\setbox0=\hbox{\'A\'Y\'AV}                  \showbox0
\setbox0=\hbox{\MakeUppercase{\'a\'y\'av}}  \showbox0
\setbox0=\hbox{V}                        \showbox0
\setbox0=\hbox{\MakeUppercase{v}}        \showbox0


So somewhere you must have a definition that is inserting extra tokens
that are breaking the kerns.