The Nikon will be a 6.5-20x. The Monarch is 44mm and the Elite 40mm. Otherwise, both are very good, and offer nearly the same excellent optical performance. The Elite is a longer than usual scope. It also has rainguard. If you ever use it in damp conditions that will be a good thing.
I have used both. Both are a touch better optically than a Leupold Vari-X III. Haven't gotten more than a glimpse through the VXIII's so can't compare it usefully.
If you see them in person, and neither has a better appearance to you or some such thing, just get which ever is cheaper. For extreme precision, I prefer the fine crosshairs available on the Monarch.