I always go back and forth on this. My kids drink a TON of nondairy milk. And I use it a lot in cereal, recipes, etc. Both kinds of milk are accessible and comparable in price, though soymilk is much easier to get at the supermarket, Target, etc. Even Walmart carries Silk! Target now carries all varieties of Silk, and their own brand, Archer Farms, even has a new line. Theirs is also fortified with calcium, B12, D2 (the vegan sourced vitamin D), and it is organic and delicious. My son resists rice milk and won’t drink plain soymilk unless I spike it with chocolate syrup. He loves vanilla flavored milk, though (or because) it contains extra sugar. I always have a tinge of guild giving my kids nondairy milk, which is so important nutritionally, when I know they are also getting plenty of sugar along with it. The sugar makes the milk palatable, and kids always want something sweet. Whether you raise them on unsweetened milk or not, as soon as they can inform you that they prefer the sugared variety, they will.
Rice milk comes in different varieties. Some store brands sell a milk that is only brown rice syrup (a sweetener) with water and fortification. A good brand will be based on real brown rice, not just syrup.
Soy milk contains more protein and healthy fat than rice milk. It has a thicker mouth feel, which some people prefer over rice milk. It is more like animal-based milk than the thinner rice milk. There are so many other varieties of milk out there now too, like almond, oat, other grain or nut, and hemp. Hemp milk is also thicker, extremely healthy, but is expensive. The other varieties tend to run more money than soy or milk too.
When I buy soymilk, I am sure to only buy organic. Nonorganic soymilk could come from genetically modified soybeans or heavily-sprayed soybean crop, and you don’t want that.
Soy is active hormonally, and this concerns people. Do we want to potentially influence the hormonal development of our kids or ourselves? Is there enough of these estrogen-like substances in our nondairy milk to actually do so?
The decisions are very difficult to make, especially with evidence from studies pointing to the beneficial effects of soybean products on disease-resistance and healthier hearts. But with so many vegan products based on soy, it is something to keep in mind.
So for now, I will buy both types of milk and switch off for my kids.