Most of my experience is with vintage pre-1990 (16xx) Datejusts, which used the 24-600, so take this with a grain of salt --
I believe the later 5-digit Datejusts (eg, the 16200) need the later 24-603. As I recall, the differences lie in each crowns' inner (stem) tube assembly. The 600 contained a screw-in (ie, removeable) inner tube assembly (if interested, you can search out my thread detailing an inner tube transplant from a 600 Twinlock to a Brevet crown) & had a slightly larger diameter, while the inner tube on the 603 was slightly narrower & was NOT removeable. That said, I believe the case-side case tube threading -- where the case tube screws into the side of the case -- is the same for both case tubes. The only difference should be the diameter of the opening inside the case tube through which the crown's inner tube assembly fits through. As long as you have the correct (matching) case tube for your crown, either crown/tube should fit the 16200. But, again, as I do not work on many 5-digit Datejusts, I cannot guarantee fitment of the 603 to your case without replacing the case tube.
So, unless someone else knows for certain or you are able to purchase a 600 with return privileges, I would suggest searching for the correct 24-603 to avoid problems or having to replace the case tube.