Better form

Adds HTML5 attributes such as "required" or "placeholder" to drupal forms.

Created by ADCI solutions team

https://drupal.org/project/elements provides some pretty similar features. How does this module differ? Is there any reason those differences can't just be patched into the elements module?

Elements module adds more HTML5 field types to build forms. But it doesn't change existing forms. You have to use form alter to do that.
Better form module changes existing drupal forms. Just install it and you will see, that you can't register now unless you input all required form fields.
That's the main difference. You don't need to do anything to use this module.