Why would a motor manufacturer offer multiple coil winding types?
A spec sheet link and actual component IDs would be very useful.

Presumably these are BLDC motors.
Compared to the other configuration:


Wye configuration 


Needs higher voltage 
Requires more cells.  
Requires lower current so lower I^2 R losses, lower spec cells, lower current FET needed.

Delta configuration 


Requires lower voltage
Requires fewer cells 
Draws more current



When optimising a design the above factors may affect design cost.  

Real world example:

I'm looking at a design that pushes current LiIon cells to their limit power wise.
Energy wise I could built the packs I need with 18650 cells.
But the top 21700 cells allow higher power per cell.
So, to achieve the same power levels with 1850 cells I need more cells and so higher voltage. 

In my case, to minimise costs, current volume pricings mean that fewer 21700 cells at lower prices overall cost less than more 18650 cells. In this case, unusually, the available energy is not important - 18650 or 21700 will both meet the needs once power requirements are met.
SO in my case a Delta wound motor with lower voltage and higher current will make sense.
Given other requirements, the opposite may apply.