Having trouble creating two shortcodes, one for logged in user and one for visitors

The code exactly as you put it in your question works fine for me and does exactly what you suggested.

To make it work I had to make sure my WP post editor was in code editor mode as HTML or Visual Editor may create extra problems:

And this is what my test code in the post editor looked like, when I had a successful test:

<!-- wp:html -->
<p>this is the content</p>

<p>more content 
[member_only]You are logged in.[/member_only]
[visitor_only]Login / Register[/visitor_only]
</p>

<!-- /wp:html -->

You can make the second shortcode a bit clearer to read by adding ! for ‘not’ on the front of the first condition, then the structure is the same as the first shortcode, and you don’t need the else:

function visitor_only_shortcode($atts, $content = null)
{
    if (!is_user_logged_in() && !is_null($content) && !is_feed()) {
       return $content;
    }
}

add_shortcode('visitor_only', 'visitor_only_shortcode');