Assuming you are a RH shooter, it is possible that the new bow has the shelf cut to or past centershot, and the other bow is not cut in as far. Many longbows are not cut to centership, while many recurves are cut to or past centershot.
You could build out the sideplate of the new bow until it impacts the same place as the old bow. This may require you to use a weaker arrow shaft.
To further fine tune, a stiffer side plate, such as leather, will move the arrow impact to the left, while a softer sideplate, such as a rug rest, will move the arrow impact to the right. But this fine tuning won't make a 6" difference at 18 yards.
If it were me, I would pick the bow I like the best and make the adjustments to the other bow, because the bow will probably perform best the way it was designed.