What does Tarski's Fixed-Point theorem give us that that Y-Combinator does't
If by Tarski's fix point theorem you mean the Knaster–Tarski fixpoint theorem, then it's widely applicable and very general. All you need is a complete lattice and a monotone function on the lattice.  There are many rather different examples of those. 
Tarski-Knaster is for example used in the coinductive definition of bisimilarity. Another application is to construct models of logical formulae (e.g. for logics with fixpoints, such as
the modal $\mu$-calculus and the various fixpoint logics that are used to characterise complexity classes). It is also used in set theory and in program analysis.

The Y-combinator on the other hand is a specific piece of syntax in the $\lambda$-calculus. You don't need to prove the existence of the Y-combinator.