"The other builder says that the chlorine pools is cheaper then SWG and would ONLY recommend SWG if anyone in my family has allergic reaction to chlorine." <-- BS ALERT

In the cells of the SWG it 'creates' chlorine and there is still the same residual in the pool. Only difference, you don't dump it in (unless shocking).

The cost factor really depends on the cost of your time. If you would hate constantly adding bleach, pucks (then fighting CYA), powdered chlorine, etc then an SWG would be worth it. Granted, you would have to monitor and adjust pH.

Also, there has been some debate on this forum regarding the potential corrosion issues with an SWG. Search the forums for saltwater damage or something similiar for more in-depth conversations on the topic.