Best way to access getPrev and getNext asset fields
If you need only one image, you can use the first() function instead of a for loop. 

I recommend to check always if a image or entry exists, befor use it. Otherwise you risk to get an error. During development you should turn on the devMode, to see all errors (https://craftcms.com/docs/config-settings). 

Here is a code example i would use in your case:

{% if prevEntry %}

    {% set asset = prevEntry.featuredImage.first() %}

    {% if asset|length %}

        {% set thumb = {
            mode: 'crop',
            width: 200,
            height: 200,
            quality: 75,
            position: 'center-center'
        } %}

        &lt;a href="{{ prevEntry.url }}"&gt;
            &lt;img src="{{ asset.getUrl(thumb) }}" class="img-responsive center-block"  alt="{{ prevEntry.title }}"&gt;
        &lt;/a&gt;

    {% else %}
        &lt;a href="{{ prevEntry.url }}"&gt;
            &lt;img src="noImg.png" class="img-responsive center-block"  alt="{{ prevEntry.title }}"&gt;
        &lt;/a&gt;    

    {% endif %}
{% else %}
    &lt;!-- There's no previous entry. --&gt;
{% endif %}