Going from this...
By the 1730s about 15 ships a year were leaving for Africa and this grew to about 50 a year in the 1750s, rising to just over a 100 in each of the early years of the 1770s. Numbers declined during the American War of Independence (1775-1783), but rose to a new peak of 120-130 ships annually in the two decades preceding the abolition of the slave trade in 1807. Probably three-quarters of all European slaving ships at this period left from Liverpool. Overall, Liverpool ships transported half of the three million Africans carried across the Atlantic by British slavers.
...the dates don't seem quite right to favour those two docks.
Also, since the slaves were generally not on board in Liverpool, why would one dock be preferred over any other?
Isn't it just a transatlantic goods shipping issue at Liverpool?
The link is here for the quote...
http://www.liverpoolinpictures.com/S..._Liverpool.htm