The problem of not cutting through the mix is mostly acoustic in nature IMHO. Most of the time, I had full PA support and a competent audio tech, so I did not worry about my sound out in the audience. I do prefer more of a HiFi, full-range type sound that is as even and focused as possible, but it should not be inappropriately "in-your-face". Of course it depends on the style of music somewhat.
IMHO the sound should be processed discretely for each location and intended use. Out in the audience, it's not necessarily desired for my sound to cut through the mix. The audio tech will dial in the EQ and compression so my sound provides the appropriate foundation, or pops out when desired.
On stage is another matter. On stage I setup my rig so my sound jumps out of the mix at the lowest possible volume. I tend to elevate my cabs to about waist level, and also tilt them back to aim at my head. The last touring rig I used had an Eden D210XLT and D410XLT, but I usually only ran the 210.
IMHO a fairly dark sound can work well in a recording. But in a live setting, the bass tends to get darker and more diffuse as the sound travels over distance. In experience, it's very common for the lows to build up into a diffuse field that mask higher frequencies. Don't get me wrong. I find really fat lows to be highly desirable, but unfortunately (IMHO) most acoustic environments don't support using a really fat bass sound live. So long ago I adopted an approach using fairly lean lows.
I also tend to run a really bright sound on stage, but my technique is pretty clean and smooth, so I don't produce a lot of unintentional gank, grind, or fret rattle. Part of my smooth sound is also the contour I use. Although my sound is bright I prefer to put a bit of a dip in the 2-4K range, which is where most of the gank lies.
Of course anyone who happens to set up to close to me on stage may think my sound is overly bright and obnoxious (if not downright painful). I tend to wear ER15s which do darken the sound a bit. I run my amp bright enough to overcome the darkening induced by the ear plugs.
The higher frequencies coming from a cab tends to be more directional than low frequencies. By tilting the cab back, the high-mids shoot up at about a 30 degree angle towards my ears, rather than straight out towards the audience. Elevating the cab reduces the lows and also puts a notch in low mids. The frequency of the notch is determined by the height. Max cancellation occurs at frequency where the distance between the driver and floor equals 1/4 of a wavelength
By limiting the volume and amount of sub-bass produced by my stage rig, it fights less with the PA. This gives the audio tech more control over how the bass sounds to the audience.