A matter of taste. Try both and see which one you like best for yourself.

Agreed. They are both solid frameworks and I've used both fairly heavily. I personally find Laravel more 'natural'. I have to refer back to the documentation in Yii far more often.

I can persuade you to use any of these two frameworks providing lots of arguments but I prefer not to do so. Try both yourself else you'll be wondering if you've made the right choice while working with one.

I would also here some experts opinions on this. How do they compare on a higher level. Say a RESTful API with JSON+HAL, HATEOAS approach, Versioning, etc. the full thing for a bigger usecase like Twitter, Tumblr, Facebook, etc.

Comparing to Facebook and Twitter is a useless comparison, because their scale causes so many edge cases. If you have that kind of scale, you can afford to hire the best in every area and build everything from scratch. Better to compare to a typical medium-sized website in a similar sector - e.g. a blog like cuteoverload.com or ecommerce site like tigerdirect.com.