Which is a dye: Ferric Acetate or Ferrous Acetate?
The gist is in the solubility products for the hydroxide precipitates of $\ce{Fe^{2+}}$ and $\ce{Fe^{3+}}$.


  $\ce{Fe(OH)3}$ doesn't really exist but is rather $\ce{FeO(OH)}\cdot x \ce{H2O}$. However the $K_\mathrm{sp}$ is calculated as $\ce{Fe(OH)3}$.


Now for the vinegar solution let's consider a somewhat "spent" solution where a lot of the acid has reacted. So consider a nominal pH of 5.5, so pOH = 8.5 and $\ce{[OH] = 3.16\times 10^{-9}}$. Let's calculate the equilibrium molarity of Fe species as "Mol(Fe) @ pH=5.5" in the table below. 

\begin{array}{|c|c|c|}\hline
 &amp; K_\mathrm{sp} &amp; \text{Mol(Fe) @ pH=5.5}\\ \hline
\ce{Fe^{2+}} &amp; 8.0 \times 10^{−16} &amp; 80.12 \\ \hline
\ce{Fe^{3+}} &amp; 2.79 \times10^{−39} &amp; 8.84\times 10^{-14}\\ \hline
\end{array}

A $\ce{Fe^{2+}}$ solution can't be 80 molar of course, but what that does mean is that all the $\ce{Fe^{2+}}$ formed will stay in solution. 

The calculations also show that a substantial amount, if not all, of the $\ce{Fe^{3+}}$ created will precipitate. The precipitation does lower the pH, so the equilibrium values are indeterminate without knowing the concentrations of the acetate anion and the nominal concentration of $\ce{Fe^{3+}}$ (amount dissolved plus amount in the precipitate). However looking at the overall reactions, it wouldn't seem that the pH could be lowered much. 

\begin{array}{c c c c}
 &amp; \ce{2Fe + 6H+} &amp; \ce{&lt;=&gt;} &amp; \ce{2Fe^{3+} + 3H2} \\
 &amp; \ce{2Fe^{3+} + 6OH- } &amp;\ce{&lt;=&gt;} &amp; \ce{2Fe(OH)3} \\
 &amp; \ce{6H2O} &amp; \ce{&lt;=&gt;} &amp; \ce{6H+ + 6OH-} \\ \hline
\text{Overall} &amp;\ce{2Fe + 6H2O} &amp; \ce{&lt;=&gt;} &amp; \ce{2Fe(OH)3 + 3H2}\\
\end{array}

A further consideration here is that oxygen from the air, which dissolves into the solution, can oxidize $\ce{Fe^{2+}}$ to $\ce{Fe^{3+}}$. 

Now I'd assume that it is the $\ce{Fe^{2+}}$ salt that you'd really want since that salt could diffuse into (soak into) whatever you're coating the solution with. The $\ce{Fe^{2+}}$ would then be oxidized to $\ce{Fe^{3+}}$ in the interior of the item.  The $\ce{FeO(OH)}\cdot x \ce{H2O}$ on the other hand would just sit on the surface of the item like a paint.