Without seeing the result and knowing your exact technique, my best guess is that you're not using enough liquid, or that you're using heat that's too high. High heat will essentially fry the onions, like you would expect by dropping chicken or potatoes into a pan full of hot oil.
Properly caramelized onions should take at least 20 to 30 minutes, I try to go for an hour whenever time permits. I actually stir as little as I can without allowing them to sit long enough to burn. Over-stirring shouldn't be a problem; under-stirring may be.
To start, you want the bottom of the pan to be covered with a thin layer of oil, and then make sure you stir the onions very well to coat them completely right after you toss them in. Begin with the pan on medium-high heat to get the oil up to temperature, once it ripples and you put the onions in you can lower it quite a bit. I rarely put it above 5 (out of 10, glass-top stove), and if I see things going crispy, I'll often drop it to 4. I'd rather take more time and have softer onions.
Are you adding any liquid along the way? Sometime, when doing large batches, 15 minutes in I find that I don't have enough oil in the pan, and I can see them starting to crisp up a bit more than I'd like. When that happens, lower the heat a notch, and add a touch more oil (or, as I prefer, a cube of homemade stock) to the pan. It'll take some practice, but eventually you'll be able to know how much liquid to use instinctively. The reason I prefer stock for my "second add" is because I know the stock will evaporate off, as mentioned in the question you linked to, you don't want to be pouring off flavor at the end of the cooking time, so evaporation is a good thing!
If you're using cast iron, I recommend trying stainless steel, I get much better results with the latter than the former. I'd guess that it's because I can dynamically regulate the temperature better with the stainless steel - with cast iron, once you realize you're at too high of a temperature, it's hard to lower it quickly.
If you need a step by step guide to start you off until you get a feel for everything, there is a great guide here and another here. The difference is that one recommends 1 teaspoon of oil per onion; the other uses 3 tablespoons per onion. I find that for my kitchen, it's somewhere in the middle (I just eyeball so I can't give you an exact number, unfortunately) - but if you try both methods on your stovetop you should be able to use that data to determine the right amount for you.
The secret to really crispy skin has everything to do with rendering the fat that lies directly under it. Once that fat has removed itself from the skin, a little high heat will crisp it up perfectly. If I am creating a roast chicken, I normally remove it from the packaging and allow it to sit uncovered in the fridge for at least overnight, longer if I have the time. Then I start the chicken low to render the fat, you have to cook it at a minimum of 178F (80C) to remove the most fat. Once the fat renders out, which is going to vary depending on the temp you start the chicken at, you crank the temp to the 450 to 500F range and baste regularly.
To maximize the skin that will crisp you want to make sure that your chicken isn't sitting inside the fat while it cooks. I normally use a inset rack to keep the chicken above the fat but you don't have to. The other component to crispy skin is cooking the chicken uncovered.
Best Answer
Both crispy and caramelized onions are cooked for a long time, and will be very brown. However, they are cooked slightly differently.
Caramelized onions are usually cross-cut on the onion to release its moisture, and then cooked over very low heat in a crowded pan, stirring infrequently, so that they gradually release their sugars and liquid and it turns to caramel. Depending on the onions and desired result, you may even cover them, an add a little liquid and/or sugar. The end result is very soft and very sweet.
Arabic-style crispy onions are cut pole-to-pole in order to avoid rupturing cells in the onions. They are then fried over medium heat in an uncrowded pan, stirring regularly. This lets them dry out and become brown and crispy, even burning on thin ends. These onions should be a mix of crispy and chewy, and more savory than sweet.