Good question! Unfortunately, there is no right answer.
It all depends on what your experimental needs are. Both these transfection methods involve getting the foreign (target) gene into the cells. In transiently transfected cells, the foreign DNA does not integrate into the host genome and as such it does not replicate and is eventually lost through cycles of cell division over several days. Transient transfection is good if you have relatively small requirements for rAb and if you need it fast. Transient gene expression results in short term recombinant Ab production, typically 6-10 days from the point of DNA transfection. HEK293 cells normally achieve higher transfection rates and higher yields with PEI which is inexpensive and resulting in lower overall production costs.
Stable transfection also begins transiently but through a process of careful selection and amplification, stable clones are generated. In stably transfected cells the foreign gene becomes part of the host genome and is therefore replicated. Descendants of these transfected cells, also express the foreign gene, resulting in a stably transfected cell line. Because the stable transfection of cells is a longer and more arduous process, it is practical for rAb production on larger scales. During initial selection process when research quantities of rAbs are sufficient (10-1000 mg), rapid methods of rAb production are required and so large scale transient expression is routinely used. For large scale production of therapeutic antibodies, stable gene expression is the preferred option as it allows for greater process consistency and control of the final product quality.