No question - the nuclear test is faster. Proponents will say that it is more accurate . . yet years ago, I did comparative moisture content (lab vs nuclear) and on our crushed base course, the actual moisture content was 0.7x the nuclear content. This is why Ron states that on a particular site (assuming a big one) you would do a comparative study of the two - and this doesn't always work especially if your operators of both sand cone and nuclear testing are less than honest . . . .
I prefer the sand cone or the rubber balloon method - but, as pointed out, you will need to do drying in an oven (min 18h or standard 24 h) or a microwave (speedy moisture is also used but it should also be "checked" and isn't wholly reliable on all types of soils). In clays, you might consider using the drive tube sample (min 100 mm diameter).
My single caution - regardless of what test you use: ALWAYS and I mean ALWAYS check to ensure that the test result is on the correct side of the zero air voids line. If the manure hits the fan, you will be glad you did.