Does the HTML5 required attribute have the same accessibility affect as aria-required for an ARIA defined widget?

For pages created using  HTML5 markup should the HTML5 required attribute be used instead of aria-required for ARIA widgets?

For example the following example of a required gridcell:

Using  HTML5 required attribute:

<div role="grid">
  <div role="row">
    <div role="gridcell" required></div>
  </div>
</div>

Using ARAI aria-required:

<div role="grid">
  <div role="row">
    <div role="gridcell" aria-required="true"></div>
  </div>
</div>

Jon