CBSE and ICSE are nation wide syllabus available across all states, where as state syllabus varies from state to state.
CBSE and ICSE have the same syllabus through out the nation, so it does not matter even if you get an inter-state transfer, because the syllabus is same through out India.
State syllabus is simple as compared to the other two but then you need to learn the state language in the state syllabus, whereas in CBSE you need to learn English throughout, Hindi till 8th grade, then you get to choose your language between Hindi or Sanskrit for your 9th & 10th grade. Once you choose your language in 9th grade, you will have to learn the same language in 10th also.
Apart from these difference CBSE students get the advantage of selecting language in which the subjects can be taught, i.e either Hindi or English. Now this purely depends on the majority, if majority of students choose Hindi then the medium of teaching and examination will be Hindi.
If we compare between CBSE and ICSE then there is not much difference, except that standard of ICSE is bit higher than that of CBSE at the same time it is considered to be tougher.
After your 10th grade you can change from CBSE to ICSE or from ICSE to CBSE, but the general trend seen is that the results of CBSE is much better than ICSE.
Another advantage of CBSE is that, the syllabus for CBSE is the basic syllabus for various entrance exams like IIT-JEE, AIEEE etc.
Where as state syllabus is the syllabus for state wise entrance examination, still it is considered that if a student is from CBSE he / she can easily tackle the state entrance exams.