[Tex/LaTex] Why are bent arrows with arrow tips not symmetric in TikZ

Question

They say a picture says more than a thousand words.

Is there a good reason why TikZ draws the arrows as skewed as in the left image? Is there any easy way to get good-looking, symmetric arrows as in the right picture without manually positioning the arrow tips?

Note: The line overlaps the fine tip of the arrows in the right image. This is not intentional, but adding shorten >=2pt also messes with the bend of the line.

Here's the code that produces the image above (without the captions).

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[>=latex]
    \node[draw,circle] at (0,0) (A) {A};
    \node[draw,circle] at (1,0) (B) {B};
    \draw[->] (A) to[out=45, in=135] (B);
    \draw[->] (B) to[out=-135, in=-45] (A);
    \draw[help lines] (0.5,0.5) -- (0.5,-0.5);
\end{tikzpicture}
\begin{tikzpicture}[>=latex]
    \node[draw,circle] at (0,0) (A) {A};
    \node[draw,circle] at (1,0) (B) {B};

    \draw (A) to[out=45, in=135] (B);    % Draw nice line
    \draw[<-] (B.135) -- ++(-0.1,0.066); % Add arrow tip

    \draw (A) to[out=-45, in=-135] (B);  % Draw nice line
    \draw[<-] (A.-45) -- ++(0.1,-0.066); % Add arrow tip

    \draw[help lines] (0.5,0.5) -- (0.5,-0.5);
\end{tikzpicture}

\end{document}

Answer 1

The choice latex is a bad idea because it's not possible to get a correct result. The size of the arrow is to big . Look at the result of your "fine" attempt

\begin{tikzpicture}[>=to]
  \node[draw,circle] at (0,0) (A) {A};
  \node[draw,circle] at (1,0) (B) {B};
  \draw[->] (A) to[out=45, in=135] (B);
  \draw[->] (B) to[out=-135, in=-45] (A);
  \draw[help lines] (0.5,0.5) -- (0.5,-0.5);
 \end{tikzpicture}    

In the next code outer sep=0pt is necessary

 \begin{tikzpicture}[>=to]
   \node[draw,circle,outer sep=0pt] at (0,0) (A) {A};
   \node[draw,circle,outer sep=0pt] at (1,0) (B) {B};
   \draw (A) to[out=45, in=135] (B);
   \draw[<-] (B.135) -- ++(-0.001,0.0009);
   \draw (A) to[out=-45, in=-135] (B);
   \draw[<-] (A.-45) -- ++(0.001,-0.0009);
 \end{tikzpicture}