According to the USDA PLANTS database (plants.usda.gov), there are eight species of dogwood and ten of viburnum to be found in this area.  All have opposite, simple leaves (except the pagoda dogwood, which has alternate leaves).  All are small to medium sized understory trees or shrubs.  Some species have distinctive leaves,

Viburnum acerfolium (maple-leaved viburnum)

but most have very similar leaf shapes.  The dogwood leaves have different venation from the viburnums.

At first glance viburnum and dogwood flower clusters look alike, but the flowers themselves are quite different.

Viburnum dentatum (southern arrowood)

Viburnum prunifolium (blackhaw)

By the way, the blossom of the ubiquitous flowering dogwood (Cornus florida) is not actually a flower; those four showy petals are bracts, surrounding the tiny flowers in the center.  (A bract is a modified leaf that looks like a flower.)

 Cornus alternifolia (pagoda dogwood)

Viburnums are in the Caprifoliaceae (honeysuckle family), while dogwoods are in the Cornaceae (dogwood family).  Despite the apparent similarities, you have to go a few steps up the taxonomic ladder to find the common relation (which is the class Magnoliopsida, dicotyledons).