inorganic chemistry - Which is more amphoteric: zinc or copper hydroxide?

$\ce{K_{a} ~Cu(H2O)_6^2+}{=~5*10^{-7}} $

$\ce{K_{a} ~Zn(H2O)_6^2+}{=~2.5*10^{-10}} $

Given this information, which forms a more amphoteric hydroxide?

My reasoning is that copper hydroxide is more amphoteric than zinc hydroxide. My reasoning is that because $\ce{K_{a} ~Cu(H2O)_6^2+}$ > $\ce{K_{a} ~Zn(H2O)_6^2+} $, $\ce{Cu(OH)_2}$ should be more amphoteric because it will probably have the bigger $\ce{K_{a}}$. This fulfills half of the definition of amphoteric - behaving as both an acid and base.

But how do I compare the base strengths of $\ce{Zn(OH)_2}$ and $\ce{Cu(OH)_2}$? I need to, because being amphoteric means the substance acts as both an acid and a base!

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Consider the following:

$1. ~{K_{a1}:} ~\ce{Cu(H2O)_6^2+ + H_2O -> Cu(H2O)_5(OH)^+ + H_3O^+}$

$2. ~{K_{a2}:} ~\ce{Cu(H2O)_5(OH)^+ + H_2O -> Cu(H2O)_4(OH)_2 + H_3O^+}$

$3. ~{K_{a3}:} ~\ce{Cu(H2O)_4(OH)_2 + H_2O -> Cu(H2O)_3(OH)_3^- + H_3O^+}$

Basic character of copper hydroxide is illustrated by the below equation:

$4. ~\ce{Cu(H2O)_4(OH)_2 + H_2O -> Cu(H2O)_5(OH)^+ + HO^-}$

The above equation, reversed, is:

$5. ~\ce{Cu(H2O)_5(OH)^+ + HO^- -> H_2O + Cu(H2O)_4(OH)_2 }$

This equation is very similar to $~{K_{a2}}$ except that the base is hydroxide ion instead of water.

We can write a similar equation for zinc hydroxide:

$6. ~\ce{Zn(H2O)_5(OH)^+ + HO^- -> H_2O + Zn(H2O)_4(OH)_2}$

Let's compare equations $5$ and $6$. We can expect $5$ to be a larger extent reaction than $6$ because hydrated copper ion is a stronger acid than hydrated zinc ion to start with. So:

${K_{rxn5} > K_{rxn6}}$

And therefore,

${K_{rxn4} < K_{rxn7}}$

$7. ~\ce{H_2O + Zn(H2O)_4(OH)_2 -> Zn(H2O)_5(OH)^+ + HO^-}$