Stem length won't impact trail, wheelbase or rake (offset) at all. But it changes the amount of hand movement on the bars to degrees of steering input. The BMC has a steeper HTA, so it will have tighter steering if both have the same fork rake (offset), which I would wager that they do. So if you use a very short stem, it means more degrees of fork turn for the same hand input, on a frame that is probably already twitchier than the C'dale.

Realize that one man's responsive is another's twitchy, so it may all be meaningless.

They make stems in all sizes because people come in all sizes. Short stems tend to be used on small frames, and long stems on larger frames, and I would assume this is because statistically normal people of each height fall into measurements that meet a lengthening top tube, seat tube, and stem for each increase in frame size. I'm probably not saying that well. I ride 58's or 60's (L or XL). Every one I have ever looked at started with a stem of 120 or 130 as stock. If I tweaked one, it was by a cm, or a few degrees. No frame I tried required dramatic move from what it was originally built and specced as.