It's more a question of what their capabilities are, vs. the capabilities of other markers, and the desired results of the artist.
Water-based markers, such as SU! and Tombow, are wonderful, high quality markers that work well for water-color type techniques and for coloring directly onto the rubber stamp, making it easy to omit parts of an image, or multi-color different parts of the image, such as a solid one (as opposed to an outline), prior to stamping.
The softness of the brush tip makes it easy to color right over thermal embossed lines, without causing damage to the image; the embossing repels the water-based ink, and if there is any residual ink on the embossing lines from coloring over them, you can quickly blot that way with a tissue.
They are not fade-resistant, will bleed out when moistened, and if your finger tips have any moisture on them at all (from lotion, natural skin oils, etc.), it can re-activate the marker ink, and you may end up with undesirable transfer to other areas of your project.
Because they are water-based and most papers are not designed to withstand water-based mediums (except for watercolor paper, etc.), if you repeatedly color over a section, it can deteriorate and break down the paper fibers, resulting in what is referred to as "pilling".
The same thing can occur if using a blender pen (designed for use with water-based markers), in conjunction with the markers.
They are designed to be disposable, and the nibs cannot be replaced; therefore they are much less expensive. Some folks do refill them when they run dry, using matching dye-based ink pad reinker. I've never tried this personally, so I do not know how effective it is.
Copic markers are alcohol-based. Richly saturated in color, but, because of the alcohol content, it evaporates almost instantaneously; no wet finger transfer issues to worry about.
They are blendable and you can achieve beautiful shaded effects using two, sometimes 3 colors, or in conjunction with good quality colored pencils, too! Many artists combine them together to achieve stunning results. The Copic "blender" pen is somewhat of a misnomer; it works more for pushing color around or "extracting" or "bleaching" out color--kinda like an eraser, altho if you used a mid to dark color, you may not be able to "erase" all of it from the paper surface.
The alcohol ink tends to bleed through most papers, unless you are using Alcohol Marker Pad Paper, so Copic colored images are best matted/layered, as opposed to single-layer cards. Water-based would be preferred for single-layer cards, because it *typically* (not always, tho) won't bleed through the paper, unless you are heavy-handed with the coloring.
Copics can be used on metal (I use them to tint my brads and other hardware), and other non-porous surfaces such as plastic, but it is best to test first, to see if you will achieve the results desired.
Like water-based, they are not fade-resistant, and whatever is in the alcohol ink tends to "eat off" any thermal embossed lines, so don't color over the embossed lines, but, within them
, to avoid that happening.
Copics are refillable, and the nibs can be interchanged/swapped out and/or replaced when worn, making them a "life-time" marker; you will never have to throw the pen itself away, just purchase reinkers or new nibs when needed.
Copic Original and Sketch are designed to work with the Copic Airbrush system, and while I haven't tried it yet, personally, some awesome affects can be achieved with it.
Because they are alcohol-based, you can color over and re-work/blend any area of the paper repeatedly, and it will not deteriorate or break down the paper fibers!
So, it's not a matter of Copic markers being "better" than other markers, but, what kind of application you are needing, and which best serves that application.