The salient difference between each other is that 想 is prone to be used as a verb, while 念 both verb and noun.
As a verb, 念 is to miss
<e.g.> We miss you very much. 我們老(/lao3/: always) 念着你.
In the sentence, 念 and 想 are interchangeable, not to mention you can use 想念 in the context.
But 想 carries meanings much more than to miss. You can think over a problem(想個問題), find a way out (想辦法), recall the past event (想過去), and even make a prediction (I don't think he'll be coming today, 我想他今天不會來).