The heat carrying capacity of 15mm copper is around 10kw depending on length, flow rate and temperature drop.
As Quality said you can work it out with the formula
litres x deltaT x specific heat capacity of water/seconds in an hour
eg 200 x 50 x 4.186/3600 = 11.63kw assuming starting from cold.
So it would take 11.63kw of energy to raise the temp of 200 litres of water by 50 deg.
By transposing the formula you could work out how long it would take to heat 200 litres with 10kw
200 x 50 x 4.186/10=4186 seconds (nearly 70 minutes)
Compare that to a coil connected to 22mm where the heat carrying capacity is around 22kw.
200 x 50 x 4.186/22=1903 seconds (about 32 minutes)
Transposed again
seconds x kw/deltaT x 4.186 = litres
eg 1903 x 22/50 x 4.186 = 41866/209.3 = 200 litres
Play around with the numbers and see what you get (you can change everything except the 4.186)
This all depends on what size boiler, what type system, flow rates, coil capacity etc.
Few cylinder manufactures actually state the reheat times using the coil as there are so many variables, rather they quote the coil surface area.
If you have a 15kw boiler on an S plan the flow of water would be shared with the rads and the cylinder return would most likely have a balancing valve fitted so in reality 15mm would do for the hot water.
A 24kw boiler with a divertor valve system (which would allow the full capacity to go to the cylinder) would be better with 22mm primaries.
It is all horses for courses.
Work it out to your (the customers) requirements and fit it to suit.
Enough brain work. I'm off to bed