The main difference will be the phase current, in wye connection the phase current is the same as the line, in delta phase current is square root of 3 of line current.
Using delta connection in a motor is very usefull on oscillating loads, or reciprocant machines such as compressors, line current will be more balanced, some cases you have to pay more for having the possibility of a delta connection in a motor, every phase is able to handle full voltage