Good question. Both are evergreen and have the Christmas tree (pyramid) shape and they both would make a nice addition to any landscape if you have enough room. Southern Redcedar, Juniperus silicicola, can grow to 40 feet tall with a 25 feet spread. It tolerates most any kind of soil and light conditions – full sun to light shade. Southern Redcedar is very drought and salt tolerant. It has very few insect issues but there are a few fungal diseases which can cause twig die back of leaf galls. Most of the diseases can easily be pruned out and controlled without chemical applications. Arizona cypress, Cupressus arizonica var. arizonica grows to the same height and spread as the Southern Redcedar, likes similar planting conditions although we are not sure about its tolerance for salt spray. Arizona cypress has a slight bluish cast to the leaves especially on new growth. It has no real insect enemies but has been known to develop blight in cool, humid conditions as well as stem canker. One big difference, Southern Redcedar is native and has been known to attract birds while Arizona cypress does not. I don’t think you could make a mistake by planting either one but I like the idea of having a native tree in my yard which is able to supply food for birds. But don’t let me influence your final decision!
Southern Redcedar: http://edis.ifas.ufl.edu/st326
Arizona Cypress: http://edis.ifas.ufl.edu/st222