When I took the handgun class at Gunsite in 2001, we were taught to use the slide stop. When I took a class from a local training group with a good reputation (AWT --
http://www.awt-co.com/), they taught us to use the sling shot method. When I took a class from Louis Awerbuck, I don't recall him expressing an opinion. And I recently took LFI-1 from Massad Ayoob, and he prefers using the slide stop. And a fellow I know who is an LEO and LE firearms instructor in the Pacific Northwest also favors using the slide stop.
What I conclude from all of this is that it's primarily a matter of personal preference. I know that each camp has strong opinions in the matter, and it's possible to identify advantages and disadvantages of either method. And if you use different types of guns, it's probably best to train using the sling shot method, because different types of guns have their slide stop in different locations, but the sling shot action will be the same and work for all.
I personally favor using the slide stop because I prefer the 1911, and it's a very easy and quick action for me to hit the slide stop with my weak hand thumb, after inserting the magazine with my weak hand, as it takes its grip over my strong hand.
And then again, I can avoid the issue entirely by using my H&K P7M8 (squeeze cocker) and releasing the slide with the cocking lever.
BTW, I'm also an instructor.