I once wrestled with this issue but no more.
For one rhodium trades at $2500 an ounce versus $1400 for gold and $1700 for platinum so no problem there.
Rhodium has a brilliant, brighter, and I think undeniably more attractive finish than white gold, which has a slight tint to it due to it being made up of 75% yellow gold (think 3/4 yellow paint and 1/4 white paint and what do you get?).
Rhodium is 4 times harder than gold, so it is extremely resistant to scratching. Unless you are working on an oil rig with your 5970, you aren't going to see the white gold underneath.
Finally, as I understand it (but yet to experience it), the watch is replated each time it is returned for service so the watch is returned to as-new condition. In comparison, your YG or RG watch will more easily scratch and to clear this up must be (ever so slightly) polished down over time. (someone please correct me if I am wrong)
I have no idea whether the 5970 was also made in non-rhodium finish. If it was an issue I might decline the non plated white gold watch and go for YG or RG (and never polish it).