집에 갈래요. = "I will go home" or "I'm going home" 집에 가고 싶어요. = I want to go home. I would like to go home. 집에 가고 싶어요. 하지만 있을래요. I'd like to go home. But I will stay here. 집에 갈래요 is a little more usual than 집에 가고 싶어요.

I think there is no difference in meaning, but "갈래요" sounds like more informal and intimate like,"갈래요(wanna go)", "가고 싶어요(...want to go..., neutral)"^^' \^o^/

갈래요 and 가고 싶어요 's mean simillar. in normal situation, this two words are almost same. and there is decision in 갈래요, there is wish in 가고 싶어요. so, 갈래요 - I decided to go. 가고 싶어요 - I want to go. but sometimes, they become very different mean, especially in question. 집에 갈래요? 1. do you want to go home? (want to know either going or not to go) 2. shall we go home? 집에 가고 싶어요? do you want to go home? and these become different means in impossible or difficult situation to go back. 집에 갈래요. normally, it is not used in impossible situation. if you say this when you can't go back, it shows your decision with giving up or grizzling. 집에 가고 싶어요. normally, it is used in impossible situation very well. this sentence able to use express wish. in this case, the mean is that I wish return to home but i can't do that.

갈래 i will go/I would go/I am going (if u put '요' in the ending if the verb, it is more polite. 가고 싶어 I want to go / 가고 싶어요 I would like to go 가다 to go -고 싶다 to want to + R(desire/want/hope/like...)