JSFiddle - React, Tailwind, and code Playground

HTML

<label>
  <span>Data inicial:</span>
  <input type="text" id="data-inicial" data-date-format="dd-mm-yyyy">
</label>

<label>
  <span>Data final:</span>
  <input type="text" id="data-final" data-date-format="dd-mm-yyyy">
</label>

<button>Verificar</button>

<p></p>

JavaScript

const inicial = document.getElementById('data-inicial');
const final = document.getElementById('data-final');
const button = document.querySelector('button');
const message = document.querySelector('p');

button.addEventListener('click', event => {
	let dataInicial = new Date(inicial.value);
  let dataFinal = new Date(final.value);
  console.log(dataInicial+"::"+dataFinal);
  	message.innerHTML = dataFinal > dataInicial 
    	? 'Data final MAIOR que a inicial'
      : 'Data final MENOR ou IGUAL que a inicial';
});