The most common problem with both rice and almond milk is that they usually contain a high level of sweeteners, and most commercial rice milk also containshigh oleic safflower oil, or some other type of unhealthy oil.
Also, recently there has been a lot of research into arsenic in rice milk. Arsenic is a naturally occurring metal (so it's not like someone's tampering and adding it or anything), and your body can typically process out any that you would be exposed to, but it's much harder for babies and toddlers bodies' to do the same. The occasional glass won't hurt them, but a constant stream of it on a daily basis may contain potential for problems.
There is also not much fat or protein in rice milk, which is one of the main reasons people are encouraged to give their babies milk. You need to make sure that baby is getting enough protein and good fat through their regular diet.
If you want to go rice, your best bet would be to make it yourself, or find one that is just brown rice and water with no additives.
Almond is the better alternative of the two (in my opinion), but you run into the same issue with additives, especially sweeteners. Again it can be made by you to help avoid those unwanted extras, but with the price of almonds, that can get a bit expensive.
I'm assuming that since you didn't mention soy milk, you've already done enough research there! : )
Another one for you to think about is also Goat's milk. It is actually surprisingly close to the make-up of human breast milk. Many kids who have issues with dairy find great success with goats milk. It tends to be a much healthier alternative than cows milk in general anyway.
Or you could just bump up to a toddler formula too.
Hope that helps some!