very good article on carnatic music and Hindustani music,maya..was abt to post something similar..but u beat me to it!!
As u've rightly pointed out,the styles employed by carnatic and hindustani is different.The ragas are the same.They are sung differently.For eg,the raag yaman of Hindustani classical is called 'kalyani in carnatic music.The swar for both ragas are the same.In carnatic music kalyani is
Arohana: s re ga ma pa dha ni s
Avarohana: s ni dha pa ma ga re s
In yaman
the arohana is : ni re ga ma pa dha ni sa
avarohana is : sa ni dha pa ma ga re sa
On close observation,one wil realise that the avorohana is the same for both and both ragas have the same swar(s re ga ma pa dha ni s),but in yaman the aroha starts with ni ri ga ma,in kalyani it starts with s ri ga ma...so the execution style is different... the basic ragas are the same.Bhairav from Hindustani is same as mayamalavagowle and Bhup from Hindustani is the same as Mohanam in carnatic.
so essentially they are the same.