getAttribute retrieves the attribute of a DOM element, while el.id retrieves the property of this DOM element. They are not the same.
Most of the time, DOM properties are synchronized with attributes.
However, the synchronization does not guarantee the same value. A classic example is between el.href and el.getAttribute('href') for an anchor element.
For example:
<a href="/" id="hey"></a>
<script>
var a = document.getElementById('hey')
a.getAttribute('href') // "/"
a.href // Full URL except for IE that keeps '/'
</script>
This behavior happens because according to the W3C, the href property must be a well-formed link. Most browsers respect this standard (guess who doesn't?).
There is another case for the input's checked property. The DOM property returns true or false while the attribute returns the string "checked" or an empty string.
And then, there are some properties that are synchronized one-way only. The best example is the value property of an input element. Changing its value through the DOM property will not change the attribute (edit: check the first comment for more precision).
Because of these reasons, I'd suggest you keep using the DOM properties, and not the attributes, as their behavior differs between the browsers.
In reality, there are only two cases where you need to use the attributes:
A custom HTML attribute, because it is not synced to a DOM property.
To access a built-in HTML attribute, which is not synced from the property, and you are sure you need the attribute (for example, the original value of an input element).
If you want a more detailed explaination, I strongly suggest you read this page. It will take you a few minutes only, but you will be delighted by the information (which I summed up here).
<div>A normal div</div>
<div>A div with a custom property set directly.</div>
<div>A div with a custom attribute set with `setAttribute`</div>
The div with the custom property set directly doesn't reflect the value to the attribute, and is not selected by our attribute selector (div[custom]) in the css.
The div with the custom attribute set using setAttribute, however, is able to be selected using a css attribute selector, and styled accordingly.