Good question, but the answer isn’t quick. Bear with me please as I step though some comparisons.
Versatility
Abrasive waterjet can cut almost anything – from metal to stone to glass to composites to ceramic. Abrasive is used to cut those materials. Then we can switch to pure waterjet, without abrasive, and cut soft goods that can be cut with a knife, such as plastic, foam, gaskets, food, paper, and (if the pressure is high enough) even shim stock aluminum.
Laser and plasma cut with heat, and so can only cut materials that have the right thermal properties. Metal is almost always the target material in industry for these heat-based processes. And mild steel is almost always the metal that is cut by them. In addition, plasma can only cut things that are electrically conductive. To optimize laser and plasma cutting, change to gasses is required. No change to waterjet parameters, except speed, is usually required for any material.
Thickness
Abrasive Waterjet can cut very thin and up to 12 inches (sometimes more) of any metal, glass, stone, composite, etc. Most precision cuts are made with our Dynamic Waterjet at thickess of 4 inches or less, but rough cutting is possible for thickness well beyond 4 inches. Laser and plasma are not as versatile in thickness. They cut like a camera, only on that which they can focus on. Laser cuts very thin and up to ½ inch, with large CO2 lasers getting up to 1 inch thick today. Plasma cuts from about ¼” up to 1.5”. Beyond that thickness shops usually switch to oxy acetylene to go up to 8” as it will cut faster and thicker than plasma.
Edge Finish
Nothing cut by a plasma or laser will be as high of quality of an edge as a waterjet. We leave behind a smooth edge. No heat affected zones or mechanical stresses are introduced. That means you can have a smooth edge that does not require any grinding or finishing. Because it's a cold cutting process there is no slag, dross, or change in material properties. The plasma and laser cut with heat (we cut with supersonic erosion). Plasma and laser therefore will leave behind a heat affected zones, mechanical stresses, and, especially with plasma, dross 'drips' on the edge. Laser can minimize this heat affected zone and stress, but can’t eliminate it. That is why heat cutting is not allowed on any aerospace parts unless you completely grind away the heat-cut edge.
So, is waterjet better for everything?
No. When cutting mild steel thin sheet metal, say 12 gage, the laser will cut faster and cheaper. We can stack to come closer to laser speed, but we cannot yet equal it (yet). So for high production runs where set up time is not a problem, laser will cut your thin mild steel sheets faster. And you might stick with plasma if you cutting, again, mild steel ½" thick and you don’t need to grind away the heated surface for either cosmetic or strength reasons. In this case our waterjet will be more costly.
But waterjet is the fastest growing machine tool process in the world (per Frost & Sullivan) because it is so incredibly versatile (cut anything that comes into your shop), quick to set up (same parameters cut almost everything with just cut speed change), leaves the best edge (no heat, no stress, satin smooth), and are easy to run (software models make it really easy to program and start cutting). If you have more than mild steel in your shop, you probably need a waterjet.