Answer: There are many possible plants you could use, depending on your soil, the exposure, the budget, the time frame and the "look" you have in mind. Both of those plants would grow for you, however Leyland Cypress is a fast growing tree and ultimately grows quite large. The Manhattan euonymous is a broadleafed evergreen shrub yet it may brown and defoliate in a windy location or during a relatively cold winter. It is clippable however and thus especially useful in a smaller area.
You could also plant American holly trees, firs, or Norway spruce if you are looking for trees. Junipers (narrow upright forms such as Skyrocket or wider mid-height forms such as Grey Owl) and arborvitae would also be possibilities in well drained, sunny locations.
In a shady location you might consider large forms of rhododendron. The Otto Luyken cherry laurel would be yet another possible selection.
Finally, in some instances a fence provides the quick screening that is needed with a more predictable size, width and appearance. It can also be planted with vines for a softer effect.
I hope this gives you some ideas to discuss with your nurseryman.
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