Hi. Yes, pressure microphones (which are omnis) generally pick up more bass, and deeper bass, than pressure-gradient microphones (which are generally directional microphones).
But pickup of low-frequency sound is very room- and position-dependent as well as microphone-dependent. There's an acoustical phenomenon called "standing waves" which basically means that certain frequencies, which are related by their wavelengths to the dimensions of the space you're in, will have definite positions in the room where they're strong and other positions where they're weak. (This affects both recording spaces and playback spaces, so when you play back a recording over loudspeakers, you get both.)
Now think for a moment about the way people use omnis (which normally have to be spaced apart in order to get any stereo effect at all) vs. directional microphones (which are most often coincident or closely-spaced) and you'll see that in a spaced pair, you're "sampling" the conditions in two distinct places in the room, while with a coincident or closely-spaced pair, you're not getting much if any differentiation between channels in terms of the standing waves in the room. Also, directional microphones, by the mere fact of having one or more "null" pickup angles, filter out any standing waves that arrive at or near those angles. So one potentially large source of "cues" about the nature of the acoustic space can be lost.
Some people really don't like having distinctly different low-frequency behavior in the two channels, but it can be interesting sounding, and it could very well be a feeling that some people would miss when they don't get it from a recording. Those people will usually gravitate toward recording with spaced microphones.
--best regards
P.S.: Conceptually as well as physically, a cardioid is halfway between a pressure transducer and a pressure-gradient transducer. A pure pressure-gradient transducer would be a figure-8. It's a long-established convention to use the word "pressure gradient" to cover all the in-between patterns (cardioid, hypercardioid, supercardioid, wide cardioid, and now "Open Cardioid") as well--but strictly speaking, that is really only true for variable-pattern dual-diaphragm capsules (e.g. a Neumann U 87 or AKG C 414 operates as a pressure-gradient microphone even when its pattern switch is set to the "omni" position--you can even hear some proximity effect).
A single-diaphragm capsule with any of the in-between patterns--including cardioid--functions partly as a pressure transducer and partly as a pressure-gradient transducer. Its characteristics will depend on the mixture of these two principles that produces its directional pattern. A supercardioid, for example, has a higher proportion of its sensitivity due to pressure-gradient pickup, while a wide cardioid is the opposite.