The quick reply area isn't using the standard form output, the new thread form is. The padding comes from how the form controls interact with labels. The form CSS would need to be modified if you wanted to change this.
If you wanted to use the standard form for both, you'd need to be heavily changing the appearance of the quick reply, not the new thread form; quick reply is the one that doesn't use the standard approach as it's designed to look like posts.
Otherwise, if you want to remove the extra padding/gutters on the standard forms, you'd need to do that in the form CSS template (for specific responsive size views).