What is the perfect size for featured images attached to a blog post or a page? I advise you to choose 1200*630 pixels, which is the ideal format if you share the URL on Facebook, Linkedin or Twitter (even if their recommended size is 1024*512). You won't lose any elements from your visual due to bad cropping.
You might face an unexpected issue though, if the default size of the featured image thumbnails on your site has slightly different proportions, which could cause the image either on a grid of posts or at the top of your post (on your website) to be cropped, losing some parts of the visual, usually at the top / bottom.
Fortunately there's an easy workaround. You can download a plugin called Simple Image sizes, then change the size of the thumbnails via the media settings (to 1200*630 pixels) and regenerate the thumbnails (via the media library) to get the right proportions. You might have to change the size of thumbnails in different locations (top of posts, related posts, grid of posts,...).
This is how I adapted the sizes of the thumbnails in the WP theme I'm using for http://blog.stickpng.com You'll notice that the images have the right proportions (1200*630) in 3 different locations: the list of posts on the homepage, the top of the posts and the related posts thumbnails at the end of each post. If you share one of these posts on Facebook, you'll also get the same image, 1200*630 pixels.