I bought the dado set at the same time I bought my first TS. It was the main reason I wanted the TS. Since then I have tried every way I am aware of that they are cut, except perhaps the saw and chisel method. Saw an plane works just find when I only need one or two 'plane friendly' joints.
The dimensions of the cut (all three of them), the size of the workpiece, where the cut is on the workpiece (how far from sides/ends of the board) and the type of wood all affect my opinion regarding what the best way for me to make the cut is. For example a .25" x .25" x 24" groove in the edge of a 1"x2"x24" that is going to be used in a panel is an entirely different cut than taking a 3.5" x 3.5" x .75" cross grain rabbet off the end of a 2 by 4.
After I get to the point of deciding which tool should give the balance of resulting quality, setup time & clean up time, I give my 'mood' a chance to over rule my scientific decision on how to cut it....

I should also point out that my 'scientific opinions' aren't always accurate..

Some times I am in the mood to set up the 'power shop' in the driveway and sometimes I'm not.
The first dado cuts I made were on a 199.00 cheapo TS with the Avanti Stacked Dado Set (49.99 at the orange box). I soon found out that there are many different types of joints that use a dado, rabbet or groove.
After learning how to do them on a TS, I started looking into how they are done with routers, both table mounted and freehand/ski-mounted. Luck and circumstances dropped a Radial Arm Saw into my lap and it turned out to be the second machine I used to make that style cut on.
Table mounted routers came next. The cuts are so much faster on a TS or RAS that I really haven't done many on my Router table. At the same time, I still think there are some styles of dado/rabbet cutting that a router table would be ideal for, especially if it were left set up for that kind of cut.
There are also some cuts that I prefer do with planes and or handsaws. The smaller the workpiece, the more I prefer the safety of hand tools.