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The .50 was a scaled up .30-'06, or at least Browning said it was, and I think he should know.
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Indeed.
The shoulder angle is different, 17.5 degrees in the .30-06 vs 15.7 degrees in the 50BMG. Other than that, you'd be pretty close if you took every dimension in a 30-06 cartridge and scaled it up by 1.65 times.
It looks like there's a little more taper to the .50BMG, the base and rim diameters scale to about 1.7 times that of the .30-06.
The case of the .50BMG is proportionally slightly shorter than that of the .30-06, it's only a factor of 1.57 times longer.
Bullet diameter, Neck diameter, Case diameter at the shoulder, OAL, Neck length and shoulder length are all in the range of 1.62 to 1.68 times larger than the .30-06.