Furniture shipping can be costly and time consuming, but most professional shippers know the best practices to transport odd shaped and modern pieces. Most inexpensive modern furniture is made from particleboard rather than wood, and is made to be "flat-packed" in a disassembled state. (Indeed, such pieces have a distressing tendency to fall apart when shipped assembled.)
Antiques, however, were most often made to be put in one place and kept there. This means that moving or shipping them presents special challenges. A piece that looks solid and well-built may be of sufficient age that it is vulnerable to damage when moved.
In most cases, unless you are very experienced in such matters, you will find it safer to hire a professional with expertise in antiques to handle your furniture shipping.