How to resolve clashing definitions of \comment in comment.sty and changes.sty without affecting either's interface?

You can via \let save both the \comment-macro which underlies the comment-environment of the comment package and the \comment-macro which comes with the changes-package.

Then you can define your own \comment-macro which "looks" at the definition of \@currenvir.

If \@currenvir = comment, then executing \comment imples calling the macro which underlies the comment-environment.
Otherwise executing \comment implies calling the macro which comes from the changes-package.

Be aware that with the following example I said \includecomment{comment} so that the content of comment-environments results in visual output.

\documentclass{article}

\makeatletter
\newcommand*\UD@CommentName{comment}%
\newcommand\UDsavedcommentenvironment{}%
\newcommand\UDsavedcommentmacro{}%
\usepackage{changes}[2019/01/26 v3.1.2]
\let\UDsavedcommentmacro=\comment
\let\comment=\relax
\usepackage{comment}%[2016/07/16 v3.8]
\includecomment{comment}%
%\excludecomment{comment}%
\let\UDsavedcommentenvironment=\comment
\let\comment=\relax
\newcommand\comment{%
  \ifx\@currenvir\UD@CommentName
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
  {\UDsavedcommentenvironment}{\UDsavedcommentmacro}%
}%
\makeatother

\begin{document}
\null
\comment{A pdf comment using `changes.sty'.}%
\begin{comment}
A code comment using `comment.sty'.
\end{comment}
\comment{Another pdf comment using `changes.sty'.}%
\begin{comment}
Another code comment using `comment.sty'.
\end{comment}
Some text.
\end{document}

Here's my solution based on @Ulrich Diez's answer, the main differences being the use of \@undefined instead of \relax and a simpler if-then-else statement:

\documentclass{article}

\makeatletter

\usepackage{comment}
\let\wfs@comment@comment\comment
\let\comment\@undefined

\usepackage{changes}
\let\wfs@changes@comment\comment
\let\comment\@undefined

\newcommand\comment{%
    \ifthenelse{\equal{\@currenvir}{comment}}
    {\wfs@comment@comment}
    {\wfs@changes@comment}%
}

\makeatother

\begin{document}
\comment{pdf comment 1}
\begin{comment}
code comment 1
\end{comment}
\comment{pdf comment 2}
\begin{comment}
code comment 2
\end{comment}
\end{document}

Then I copied the preamble into my package, removed \makeatletter and \makeatother, and replaced \usepackage -> \RequirePackage.