There's an odd asymmetry in the language used to describe microphones: Only pure pressure transducers are called pressure transducers, while a microphone that uses a combination of pressure and pressure-gradient response is invariably described as a pressure-gradient transducer. Pure pressure transducers are omnidirectional while pure pressure gradient transducers are bidirectional (figure-8). Any other pattern is a mixture. Cardioid is a 50/50 mix--yet cardioids are invariably described as "pressure-gradient." Go figure.
For single-diaphragm microphones, you can use the spectrum of "first-order" directional patterns as a guide to how much sensitivity a microphone will have to wind, breath noise, "popping" of consonants with close-miked vocals, proximity effect, and sensitivity to vibration and handling noise. The more toward the pressure-gradient end of the spectrum you get (supercardioids, hypercardioids and finally figure-8s), the more you'll have these problems.
So if a wide cardioid microphone is single-diaphragm, it will very likely be less sensitive to wind and breath noise than a comparable cardioid. This also applies to solid-borne noise.
The first time I recorded a concert with a pair of single-diaphragm wide cardioids, I used two different miking positions depending on the instruments and voices in each piece on the program, so I was picking up the entire mike stand, moving it, and setting it back down onto the floor. When I got home and played back the recording, there was no trace of noise at all as the stand was moved and set down onto the floor.
The above statements do not apply to electrically switchable multi-pattern microphones, which have two cardioid capsules back to back; each has the usual cardioid sensitivity to wind and breath noise and mechanical shock, so when you add them together to make an "omni" or a wide cardioid, you still have those problems to some degree. Dual-diaphragm microphones even have some proximity effect when set to "omni."
--best regards