Your I20 does not guarantee that you will be granted F1 status. The fact that the school gives you an I20 only means you are admitted to a program. You can use your I20 to apply for a change of status to F1. You can also just leave the I20 alone and do nothing. The point is having the I20 does not mean you are on F1, nor does it mean you have to use it to change to F1.
H4 is allowed to take any classes. F1 is required to take classes and be full time. So H4 can take less than full time if you can't deal with too many classes in a certain semester. In this regard, H4 is more flexible.
But H4 is not allowed to work. So if you are offered assistantship, as H4, you cannot take it.
If you just want to go home to take care of some family business, and be able to go back and take classes, without any concern of accepting assistantship, then you can go and come back as H4.
H4 is allowed to take any classes. F1 is required to take classes and be full time. So H4 can take less than full time if you can't deal with too many classes in a certain semester. In this regard, H4 is more flexible.
But H4 is not allowed to work. So if you are offered assistantship, as H4, you cannot take it.
If you just want to go home to take care of some family business, and be able to go back and take classes, without any concern of accepting assistantship, then you can go and come back as H4.