Boiling rice - drain or boil off water?

Method 2 is simply cooking rice the same way you would cook pasta, cook with rolling water until tender then strain (and rinse if needed);

It will make for rice with separated grains; some people like that over rice prepared with method 1.

I don't think rinsing off the starch will change much in regards to nutritional values of the rice.

If you have problem with burn rice for method 1, then either add a little bit more water or use a lower temperature or a heavier bottomed pan.

Remember that some rice variety will cook better with method 1 (asian rice, italian rice) and some with method 2 (long grain rice)

If you are burning your rice on method 1 you either have too little water in it, cooked it too long, or have it on too high a heat. Assuming you are using white rice the general rule of thumb is to use double the volume of water as you do rice, so 2 cups of water for 1 cup rice. You then cover and bring it to a boil and then turn it down as low as you can and cook it until the water is absorbed, this could be 10-18 minutes depending on the variety of rice you are using. I sometimes bring it to a boil on a big burner and move it to a small burner to finish. I use method 1 for all white and brown rice as once you get the technique down it's pretty much foolproof, and less muss and fuss than method 2.

If your rice is soggy with method 2 you have cooked it too long, plain and simple. All you need to do is cut down your cooking time. I use method 2 for wild rice as every variety needs different amounts of water and the packaging is usually completely wrong. Using more water than can be absorbed takes the guesswork out of it and makes cooking it more reliable.

As for the starch part of the question rinsing your rice to get more separated grains does remove some of the starch from the surface of the rice. As starch = carbs = energy this does mean you are reducing the amount of absorbable energy from the end product. However, this is vanishingly small and nothing to worry about, it's all personal choice of how you like your rice.

Boiling in excess water results in leaching out of water-soluble nutrients including starch and their loss when the cooking liquor is discarded. For example, 0.8 percent of the starch was removed on two washings of three milled rices, but 14.3 percent of the starch by weight was in the rice gruel after cooking for about 20 minutes in 10 weights of water (Perez et al., 1987). Protein removal was 0.4 percent during washing and 0.5 percent during cooking. Boil-in-the-bag parboiled rice in perforated plastic bags makes cooking in excess water simple and convenient. In the rice cooker or optimum-water-level method, the leachate sticks to the cooked rice surface as the water gets absorbed by the rice starch. The bottom layer is more mushy than the top layer.

http://www.fao.org/docrep/t0567e/T0567E0i.htm

Cooking rice is one of those things that you gain intuition the more you prepare it. Generally you should always boil off the water in your rice. In some restaurants I've worked in they will drain the rice and let it steam with the lid on for 10-15 more minutes. However, this is because we were cooking large amounts of rice quickly in giant pots, and this was the easiest way to ensure consistency in preparation with other prep cooks.

Cooking it off tends to work better for me, but if there's a lot, it can lead to mushy rice. The "two fingers" method where you start with excess water (the arbitrary "a couple of fingers width above the rice" measurement), bring it to a boil, boil off the water above the level of the rice, then lower it to a simmer, cover it and let it finish steaming, works really well.

I'm not sure the time for white rice, because that's always been a rice-cooker thing for me, but I like the results better with brown rice this way vs rice cooker on the brown rice setting. After boiling off the excess, the brown rice is cooked in about 15 minutes of covered steaming. If there's still a bit of moisture after the 15 minutes, you cook it off, fairly quickly.