That's a really good comparison! And to be honest, it seems less like a bug now but more like it was done this way intentionally. It literally seems like the animation on the 7 is slow (not lagging, but slow) at first because it's waiting for the next course of action by the user: just a single click to go home or a double click to go to the multi task screen. Due to the home button being digital it might work differently then the mechanical one (they might've set this behaviour up this way system wide for the 7 and therefore even the AssistiveTouch uses that animation too). Let's hope Apple can find a way around this because it's really annoying in real life, but they might just call this a "feature".
Could you maybe add a third animation of you actually double clicking the home button. Maybe it will make it more clear if this actually is intentional.