This is a dilemma for several parents and students.

Several things need to be kept in mind. 

IGCSE and IB, the international boards, are best suited for those students who know for sure that they're going to head abroad for undergrad. 

These boards offer a hands-on curriculum, with a greater scope for creativity than the regular Indian syllabus. Many Indian universities however, are unfamiliar with these systems. 

And the timing of the results of the International Baccalaureate in particular, is out of sync with the academic year of Indian universities and schools - and hence, they don't have their results while college admissions are going on. 

State board schools cater to a vast socio-economic spectrum. Many state boards such as Maharashtra and West Bengal have a rigorous curriculum, but their examination system, also keeps in mind the needs of first generation learners, and is tuned accordingly. The syllabus at the level of grade 11 and 12 is similar to that of the ISC and CBSE, but the questions are generally several notches below those of the central boards. 

State boards leave students underprepared for rigorous entrance examinations, but in states like Maharashtra and Rajasthan there are several integrated programs, where the school or junior college, prepares students, both for the state board examination (in class 12) and for the entrance examinations such as the IIT JEE or the NEET, for MBBS admissions. Do keep in mind, that top American and British universities are often unfamiliar with the SSC and HSC certificates from State Boards, and they prefer to see a School Leaving Certificate from the CBSE or ISC system. In general, however, state board schools are relatively affordable, and the student body is a more accurate microcosmic representation of society that what one would find at several CBSE or ICSE schools. 

The biggest confusion, however, is between the CBSE and ICSE boards. 

In many of the cases, it is really the school which matters. Mayo College, Delhi Public School (RK Puram), Modern School (Barakhamba), Lawrence Schools, St. Columba's, Heritage, National Public School, RN Podar are some of India's finest schools and are all affiliated to the CBSE board.  What is unique to all these schools, in general, is that they make an attempt to do a lot more beyond the mandatory curriculum prescribed by the board. All these schools have a great emphasis on experiential learning, extra curricular activities and language skills, which goes beyond the bare minimal rubric prescribed by the board itself. 

The ICSE board on the other hand, has fairly rigorous standards in middle school as well as grades 9 and 10. CBSE students have 5 or 6 board papers, whereas ICSE students have 11 papers, in addition to practical work and project work which is relatively limited in CBSE.  In addition, the ICSE system forces a "sixth subject" such as Computing or Drama or Art or Technical Drawing, even at the grade 9 and 10 level. CBSE doesn't have any mandatory sixth subject. The difference in the standard of english is particularly stark, but some CBSE schools ensure that their kids read supplementary books and novels, in each session. 

In grades 11 and 12, the syllabus of both the boards is largely the same in subjects like Science, Mathematics, Economics and Commerce. The ISC system has a higher workload in subjects like english, computers and humanities courses. However, few ISC schools offer humanities, compared to the CBSE schools. Despite the CBSE and ISC syllabus being largely similar, from the point of view of IIT JEE and NEET aspirants, the "integrated programs" where schools have coaching for entrance within class hours, is often available only in the CBSE schools, which is why there is an annual exodus of ICSE students defecting to CBSE, after the class 10 board exam. 

The Council for the Indian School Certificate Examination, has a smaller network of schools, but a disproportionate number of heritage schools and upscale schools are still under its aegis. La Martiniere Schools, Bishop Cotton, Hyderabad Public School, Frank Anthony, Doon School, Welham Girls', Shri Ram, Lilavatibai Podar, Singhania, Rishi Valley, Jaipuria and City Montessori are some of the prominent school under its hood. The standard of english in ICSE/ISC schools is far better than those of CBSE and State Board schools. Students read the works of Shakespeare in their pure, unabridged form, in high school.

While choosing between CBSE and ICSE, it is really the school which counts. ICSE/ISC schools are often somewhat on the upscale side, have better facilities for sports and extra-curricular activities, and are more expensive for that reason. For those in transferable jobs, CBSE is a safer bet, as there will generally be no problem finding another CBSE school in a new city or town. CBSE also has a reasonably large network of schools in the middle east. The one flip side to CBSE's large network is the entry of subpar schools and teachers into the system, which often leads to poor evaluation and assessment of answer scripts and a ton of marking snafus in the board examination These things most certainly do happen in the ICSE and ISC board examinations as well, but the quality of teachers correcting answer scripts, is slightly better over there.