How can I test the value of two counters?

\thecounterA works only if the counter wasn't redefined:

\documentclass{article}
\newcounter{counterA}\renewcommand\thecounterA{A\arabic{counterA}}
\newcounter{counterB}\renewcommand\thecounterB{B\arabic{counterB}}
\setcounter{counterA}{2}
\setcounter{counterB}{2}

\newcommand\maccommand{%
  \ifnum\value{counterA}=\value{counterB}
    Just so you know, counterA (= \thecounterA) holds the same value as 
    counterB (=\thecounterB).%
  \else 
    Sorry, but the counterA (= \thecounterA) is not equal to counterB 
    (=\thecounterB).%
\fi}

\begin{document}
\maccommand

\stepcounter{counterA}
\maccommand

\end{document}

The TeX way:

\makeatletter
\newcommand\maccommand{%
  \ifnum\c@counterA=\c@counterB
    Just so you know, counterA (= \thecounterA) holds the same value as 
    counterB (=\thecounterB).%
  \else 
    Sorry, but the counterA (= \thecounterA) is not equal to counterB 
    (=\thecounterB).%
  \fi}
\makeatother

Internally \c@counterA holds the value and \thecounterA is the representation. On LaTeX level \c@counterA shouldn't be used.

Use \ifnum instead of \ifx.

\documentclass{article}
\newcounter{counterA}
\newcounter{counterB}
\setcounter{counterA}{2}
\setcounter{counterB}{2}

\newcommand\maccommand{%
    \ifnum\the\value{counterA}=\the\value{counterB}
        Just so you know, counterA (= \the\value{counterA}) holds the same value as counterB (= \the\value{counterB}).%
    \else 
        Sorry, but the counterA (= \the\value{counterA}) is not equal to counterB (= \the\value{counterB}).%
    \fi}

\begin{document}
\maccommand

\stepcounter{counterA}
\maccommand
\end{document}

You can certainly do, in plain TeX,

\newcount\counterA

\counterA=2

\ifx\counterA>2 
  Just so you know, counterA is greater to than 2.
\else 
  Just so you know, counterA is not greater than 2.
\fi

but this will compare the token \counterA with the token > and find they've different meanings, so everything up to \else will be gobbled and you'll get

Just so you know, counterA is not greater than 2.

But if you now try adding

\counterA=1000

\ifx\counterA>2 
  Just so you know, counterA is greater to than 2.
\else 
  Just so you know, counterA is not greater than 2.
\fi
}

you'll get exactly the same.

For numeric tests you have to use \ifnum; the code

\newcount\counterA

\counterA=2

\ifnum\counterA>2 
  Just so you know, counterA is greater to than 2.
\else 
  Just so you know, counterA is not greater than 2.
\fi

\counterA=1000

\ifnum\counterA>2 
  Just so you know, counterA is greater to than 2.
\else 
  Just so you know, counterA is not greater than 2.
\fi
}

will produce

Just so you know, counterA is not greater than 2.
Just so you know, counterA is greater than 2.

The conditional \ifx compares the meaning of the two tokens that follow, without doing any expansion on them.

_{If the first or second token after \ifx is either \else or \fi, TeX considers the code to be an incomplete conditionals and adds one or two “frozen \relax” tokens, as need be.}

Note, conversely, that \ifnum performs expansion, because it needs to find a <number> followed by a <relation> (one among =₁₂, <₁₂ or >₁₂) and another <number>.

Since in LaTeX the instruction \newcounter{counterA} performs also \newcount\c@counterA and the macro \value is defined by

% latex.ltx, line 2084:
\def\value#1{\csname c@#1\endcsname}

Therefore, doing

\ifnum\value{counterA}>\value{counterB}

will provide the appropriate tokens for the test. Hence your code could be

\newcommand\maccommand{%
  \ifnum\value{counterA}=\value{counterB}% <--- don't forget this!
    Just so you know, counterA (= \thecounterA) holds the same value as counterB (= \thecounterB).%
  \else 
    Sorry, but the counterA (= \thecounterA) is not equal to counterB (= \thecounterB).%
  \fi
}

Note that \the\value{counterA} is not needed. However, a % after \value{counterB} is needed, because \c@counterB is a counter register, so TeX doesn't look for an <optional space> after it. This <optional space> would be looked for and gobbled in case you use \the\value{counterB}, but this method is conceptually wrong.

In the body of the macro I used \thecounterA and \thecounterB, which expand to the current representation of the counter's values (default, decimal number). It would be wrong to use \thecounterA in the numeric test for \ifnum.