Go out and cast to see which prediction conforms to reality.
I don't have to. I've been throwing flies since 1957 and double hauling since 1958.
A good double haul will increase distance by around 30% with top casters. Check out the sexyloops "line hand in pocket" casting competition among European competitive distance casters most with national distance casting titles.
So lets run some numbers according to the formulas. Figure a tip speed of 90mph and a haul of 30 mph and a line wt of 100 gr. to keep the math simple.
without haul Momentum = 90 x 100gr or 9,000
with haul Momentum= 120 x 100 or 12,000
without haul kinetic= 90 x 90 x100 / 2 = 8,100 x 100gr/2 or 405,000
with haul kinetic= 120 x 120 x 100gr /2 = 14,400 x 100gr/2 or 720,000
So using momentum we show a 33% increase in force with the haul.
Using Kinetic energy we show a 78% increase in force with the haul.
With a little more haul speed we'd be hitting that 180' mark with a 5 wt.