What are the differences between quadrapod robots and hexapod robot ? Besides Hexapod having better stability.
Well, since quads have fewer legs and fewer servos, they are much cheaper and require less battery power.
Hexapods can lift more weight, since it has more legs.
You don't want a wide stance with a quad (unlike your pic). Watch how a dog or horse walks/runs, and you will see that the legs are really close to each other - this greatly improves stability.
Do you think it is possible / worth it to make a hexapod or quadrapod from scratch or to just buy one ready made?
The build or buy argument. The more you do custom, the more you learn and the more 'I did it myself' pride you can claim. But buying it will save you time and it will probably work better too. Cost will probably be about the same. Ask yourself what your goal of building that robot is, and the answer will come