Not well I'm afraid. I have both the LGB and AMS coaches. I believe you will find the LGB cars to be too small to run with the AMS cars. There was a post about 6-8 weeks ago with a great comparison photo. The AMS cars are massive!
I do have my 1:29 LGB Mike pulling 1:20 AMS freight cars. Since the freight cars are 1:20 and small narrow gauge cars, I think they look good together, as the NG cars seem to be about the same size as the (prototypically bigger but smaller scale) 1:29 freight cars I've seen. However, at a closer look you will see the wheels are tucked under more than the real 1:29 freight cars. I know this would bother some modelers who know these cars well, but I'm fine with it. So, I would say you need to also go with what works for you
On another note though, the 1:20 AMS passenger cars are huge, as you can see in Kevin's pictures above.