Parametrics are much more precise than graphics but also require more skill & understanding to set up well. IMO really more of a studio tool.
To me (for guitar, at least) graphic EQs are a special effect, something I'd kick in for a lead part or specialty tone (or use with a specific OD pedal) but not one that I regularly use on my overall sound.
I know some amps have 'em built in, and that can be part of your normal tone but I'd avoid changing EQ settings from one venue to another. That could mess with the way the soundman EQs your tone in the house mix - which is the most important thing since that's what the audience hears. Only the front rows hear much of your actual stage sound. (Of course, occasionally you run into a soundspace that's so weird you need to tweak things just to hear yourself... but IMO the more consistent your tone from night to night, the better it is for the soundman.)
FWIW, Source Audio makes a compact graphic EQ pedal that has presets; always thought that would be useful myself. One of my pedalboards has the Alexander Quadrant delay with presets and that's quite handy. I got spoiled using rack units for many years and kneeling to tweak delay times is no fun.
Someone mentioned paragraphics, a cool hybrid - I don't know why they aren't more popular. We had an SWR bass amp in the studio with a tunable 4-band graphic plusoverall Bass & Treble controls. I never took it on the road but that thing sounded great.
I sometimes use a tilt EQ when switching between guitars. Not to remake the overall tone but to bring the levels and ranges into the same general ballpark so the rig responds similarly. I can get the same type of drive when going from vintage output to modern axes, but the guitars still sound like themselves. For years I used an ole DOD BiFET preamp for this. Now I have a VFE Pinball, a similar pedal that also permits tuning your shelf points for the low & high bands.
