This is a matter of personal opinion, specific needs and finances. Each metal has advantages. Platinum is more expensive but requires significantly less upkeep over time. Platinum prongs and shanks do not wear away as quickly as white gold. Platinum does not require rhodium plating to maintain a white color over time. Platinum is preferred as the setting metal for delicate stones as its working properties allow less stress to be placed on stones during the setting process. On the flip side, large flat areas of high polish platinum tend to show scratches more readily than other metals if the surface is not burnished (a process that hardens the metal).
White gold is less expensive than platinum. There is 14KT white gold which is 58.5% gold and 18KT white gold which is 75% gold. The properties of each differ slightly. 14KT has less gold content and is thus less costly than 18KT. Both tend to have good resistance to scratching but most white gold alloys (recipes) require rhodium plating to achieve and maintain a white color. The particular alloys for many white golds result in very hard metals, which require more pressure to be exerted during stone setting. More pressure exerted equals more risk to the stone. White gold prongs will need maintenance much more quickly than platinum.
So, you should by the metal that best fits your particular situation and is best for the stone that you are planning on having set.
A good rule of thumb in choosing a diamond jewelry appraiser is if you don’t know where to go to get jewelry appraised…read your local jewelry appraiser reviews. If you only choose one item, a diamond ring appraisal would probably be your best choice. Also, if your purpose is to sell diamond jewelry, a current jewelry appraisal will help you decide a better selling price.