  The uniform Kruskal theorem extends the original result for trees to general
recursive data types. As shown by A. Freund, M. Rathjen and A. Weiermann, it is
equivalent to $\Pi^1_1$-comprehension, over $\mathsf{RCA_0}$ with the chain
antichain principle ($\mathsf{CAC}$). This result provides a connection between
finite combinatorics and abstract set existence. The present paper sheds
further light on this connection. First, we show that the original Kruskal
theorem is equivalent to the uniform version for data types that are finitely
generated. Secondly, we prove a dichotomy result for a natural variant of the
uniform Kruskal theorem. On the one hand, this variant still implies
$\Pi^1_1$-comprehension over $\mathsf{RCA}_0+\mathsf{CAC}$. On the other hand,
it becomes weak when $\mathsf{CAC}$ is removed from the base theory.
