The lives of Bach and Thyagaraja are interesting in showing how their respective cultural backdrop and worldviews shaped the music they created. Religion formed the bedrock of the best of what they produced and both had testy relationships with patron-kings, that is where the similarities end.
Thyagaraja's, May 4, 1767 - January 6, 1847, biography, http://en.wikipedia.org/wiki/Thyagaraja, is very sketchy and mostly mythical. He was, in the tradition of most religious nihilists in India, a wandering mendicant with no thought of tomorrow, just a soul lost in servicing the Lord with his musical talent (or genius!!). He would go through streets singing his verses, not really begging but nevertheless with a bag slung across to take in whatever alms that passers by drop in. Its called "unja viruthi". A westerner can relate the life style to something like that of St.Francis of Assissi.
Bach's, 31 March 1685 [O.S. 21 March] – 28 July 1750, http://en.wikipedia.org/wiki/Bach, life is very well documented, his compositions are catalogued with historical accuracy and importantly we know with greater accuracy his moods for many of his compositions. While Bach wrote a huge body of compositions with religious themes he was at home with composing secular music too. Bach's "Well Tempered Clavier" exemplifies Western Classical music at its best from the perspective of music being written "for" an instrument.
Analysed from chronlogical perspective its interesting to note that Thyagaraja follows Bach. In Thyagraja's time Indian music had its rich repertoire of musical instruments, by the 1790's violin too made its entry. Yet there is no role for instruments in Carnatic music. The composer does not write music in its entirety, the art of symphony remains unkown to Carnatic musicians to this day. Quite often the so called accompaniments are sheer experimentations with pathetic quality. Not having been exposed to what true "symphonic" quality in music is Carnatic musicians are totally unable to identify the "limits" of their music. MS Subbulakshmi in her UN performance made a caricature of herself trying to sing in English with a western compsition for Piano. The singer and the composer outdid each other in plumbing the depths of mediocrity. The evening was saved by the audience which maturely overlooked that attempt and appreciated the queen of melody when she explored the heights of melody.
Bach had to seek work, having had to seek work he had to time and again prove his mettle and his genius flowered through such vicissitudes. Thyagaraja, rejecting gainful employment churns out soulful songs. Having failed to engage with the world he is ignorant of anything beyond the provincial hamlet of Thiruvarur, the western impulse of exploring, crossing boundaries, creating new forms are yet unknown to the feeble Oriental mind. Thyagaraja lived and died in a small town. Bach goes hither and thither between Weimar, Leipzig, Kothen etc. He goes from conducting church music, to being music teacher, to meeting the challenge of a monarch. The fugues composed in response to a challenge by Frederick of Prussia remains one of the greatest compositions of western classical music and is considered the pinnacle of musical genius, man at his best. Biologist Lewis Thomas, when asked what signals can we send to outer space hoping aliens would pick it up, replied "lets send Bach's fugues but then that would be considered boasting".
The genius of writing a symphony or an opera is that the composer has to imagine the entire music in his mind, how would an Oboe sound when a violin plays in the foreground while a tympani sounds in the distance and the soprano reaches for a certain high note. That calls for the highest creativity possible by man. Thats why Bach remains a composer and Thyagaraja remains a lyricist, a revered one at that.
A related concluding note would be to ponder how come productions of musical instruments is extremely professional populated by geniuses in the western world but professionalism in producing an instrument is totally unheard of in India. The names Stradivarius, Amati, Steinway all conjure up immense respect for the genius in crafting the finest of musical instruments. Tanjore is the place for producing veena, one visit to a veena crafting place makes you feel like you stumbled into a pottery place, a pottery place for fine pottery if at all one can be charitable.