If you’ve been around much Olympic Weightlifting, you know that most lifters opt for a split jerk (though more and more are moving towards a squat jerk). It’s true that you cannot lift as much weight with the push jerk, BUT it is a great movement to help improve your split jerk. Check out this article from Spencer Arnold. It is not super cheery, but illustrates the benefits of this move.
Why Push Jerk?
CrossFit Kirkwood 