I kept procrastinating on writing about this topic until I was reminded of it with this article from Slate. You see, I've never regularly practiced squatting (I only used the flat toilets during long road trips here in Saudi) as I was raised using the standard toilet and so my body simply grew incapable of comfortably squatting. However, a while back the toilets stopped working in my office and I was forced to resort to the Eastern-toilets. And I must admit that everything stated in the Slate article is correct. Without getting too graphic, let's just say that everything simply 'flowed'.
The Wikipedia page on flat toilets lists a few of the health benefits. In addition to it being physiologically healthier, these toilets are environmentally safer. They don't require an obscene amount of water to flush with the more traditional toilets letting natural decomposition do most of the work (see: Humanure).
For those curious, here's a hilarious yet educational video on the Do's and Don'ts of squatting:
(YT link) (h/t American Bedu)
Finally, if you do decide to go down this route, you can look as happy as this lady!