They're not quite the same.
'Inconsiderate' means not thinking about other people's needs in general. If you finish all the bread in the house and don't buy any more, so that when your family/housemates come home tired and hungry and there's nothing left for them to eat - this is inconsiderate. Inconsiderate people are often thoughtless and self-centred in the the way that they behave.
'Insensitive' means not thinking about the feelings of others. For example, if your friend is upset because her boyfriend has just broken up with her, it would be insensitive of you to tell her how happy you are with your new boyfriend. Insensitive people are often thoughtless and tactless in what they say.