Equipment capabilities aside for a moment, as a digital photographer, one has some choices that are touched upon in the preceding post ... but I wouldn't reduce it to two options ... Here are two of the choices mentioned and my own thoughts:
*** Shoot RAW or JPEG?
If one chooses, RAW - regardless of any other choices - one can set the white balance after the fact ... but it doesn't hurt to get it right in the camera.
If one chooses JPEG - regardless of any other choices - one needs to get the WB correct in the camera as it is much tougher to fix in post.
*** Use strobes or ambient light?
This is a different and independent decision. One can shoot RAW + Strobes, RAW + Ambient, JPEG + Strobes, JPEG + Ambient ...
One's strobes' color temperature is what should determine the WB setting when using strobes ... whether shooting RAW or JPEG, the color temperature of the strobes is what you are seeking to match in your processing - whether in camera or in post. If using strobes and shooting RAW, you can defer this to post ... if using strobes and shooting JPEGs, it is best to get this right in the camera.
If shooting with ambient light, WB is depth (and distance) dependent ... but again, if shooting RAW there is no urgency other than post-production efficiency to getting it "right" in the camera and if shooting JPEGs one needs to get it as right as possible in the camera.
When shooting with ambient light at depth, filters are a great help in achieving a good white balance.