What effect does the number of coil turns on an electric stove heating element have?
IMHO:

The number of coils does make a minor difference in the time it takes to heat the burner; on the one with the extra coils, the coil's elements are usually smaller and therefor heat faster and cool faster.  The extra turns make up for the smaller coils.

You have to look at the ratings of the different coils.  Are they the same wattage? 
Are the connections the same? (will the new one plug into the existing stove?