There are several considerations. First of all, the Pro Type will fit into a narrower gap than the V-Shaped. The Pro Type requires a minimum gap of 1/16" while the V-Shaped requires a minimum gap of 1/8". You have to have a good bit of wiggle room to use the V-Shaped.
The V-Shaped is stiffer than the Pro Type. It may provide a better seal in some applications.
The V-Shaped is available in narrower widths while the Pro Type is available in wider widths.
The V-Shaped must be shipped in long boxes as it cannot be rolled.
For double hung windows, if you make the top sash operable, you must contend with the pulley & weight system. If you use the Pro Type weatherstrip, you must cut a D shaped cutout in the weatherstrip for the pulley, keeping the un-nailed edge of the weatherstrip continuous. If you use the V-Shaped weatherstrip, if your window is thick enough, you can sometimes keep the weatherstrip to the parting bead side of the pulley wheel and avoid interference. The 1/2" and 5/8" wide V-Shaped weatherstrip may be best suited for this.