Composition and improvisation
Carnatic music is built around composed songs. The kriti, in pallavi, anupallavi and charanam, is the heart of a concert, and much of the repertoire comes from Tyagaraja, Muthuswami Dikshitar and Syama Sastri, the Trinity of the late 18th and early 19th centuries. Improvisation, called manodharma, happens within and around the compositions, as alapana, niraval and kalpanaswaram.
A Hindustani performance gives more of its time to the slow unfolding of a raga, with a short composition, the bandish, as its frame. The main vocal forms are dhrupad and khayal, with lighter forms such as thumri. Styles pass down through gharanas, schools linked to particular families and courts.
Ragas and scales
Carnatic ragas are organised by the melakarta system: 72 parent scales, from which the other ragas are derived. Hindustani ragas are commonly grouped into thaats, a scheme set out by V. N. Bhatkhande in the early 20th century. In Carnatic music the gamaka, the oscillation or slide on a note, is central to how a raga is recognised.
Rhythm and instruments
Both use tala. A Carnatic singer keeps the tala visibly on the hand, and a concert is usually accompanied by violin and mridangam, sometimes with ghatam or kanjira. Hindustani vocal music is commonly accompanied by tabla with harmonium or sarangi, and dhrupad traditionally by the pakhawaj.
Which one should you learn?
Both are complete, lifelong disciplines, and neither is easier. Many families in Telangana and Andhra Pradesh choose Carnatic music because its songs are largely in Telugu, Sanskrit, Kannada and Tamil, and the Telugu composers Tyagaraja, Annamacharya and Bhakta Ramadasu are part of everyday life. If you want to sing those songs, Carnatic training is the direct route.
RAAGA teaches Carnatic vocal music. If you are looking for Hindustani classes, ask a school whether it teaches that tradition specifically.