I have older versions of both: Primus OmniFuel (no simmer valve) and a Whisperlight.
The differences between the 2 are merely trade-offs.
The Primus burns anything: propane, white gas, diesel, etc. A somewhat useful feature, but, for me, I almost always have white gas. It melts snow and boils water about the same as the Whisperlight.
It's loud compared to the Whisperlight. And despite the flame deflector, it still creates a hot spot in one area of a pot....not great for simmering rice, for example.
It's quiet and it bathes the bottom of the pot in flame, eliminating a central hot spot.
The fuel line is short and fixed in relation to the stove. On rocky ground or other uneven surfaces, it can make it awkward to get the stove level as the weight of the fuel bottle can cause the stove to tilt. It doesn't burn the variety of fuels that the Omnifuel does, but for me, it's a non-issue. MSR parts are much more common than Primus parts.
Overall, there's not much to choose between the 2 stoves, but if I had to, I'd pick the Whisperlight for the non-scorching aspect.