Well, it all depends on what you mean by significant.
This is completely unacceptable. The barrel should not move at all when fully in battery. If it's just sitting in the slide with the slide off the gun, there might be some movement. However, with the barrel properly installed in the slide, the slide properly installed on the gun and fully forward (in battery), the barrel should not move at all. If it does, your barrel does not fit the slide and I would recommend not shooting it. It might work, but it's certainly not right.
For practical purposes, the accuracy I see from the 9mm barrel in my .40S&W gun is decent. I would say it's as good as the .40S&W barrel. This is all with cheap ammo and not further than 10 yards and from a standing position. I have no checked it from a rest.
Now, there are some differences. Let me show some pics:
Here is the .40S&W installed in the .40S&W slide.
Here is the 9mm in the same slide.
See the gap in the 9mm barrel hood? Here are the measurements of that same spot for both barrels:
.40S&W
9mm
Even so, when installed properly, and fully in battery, it should not move. Mine doesn't.