Though their lifetimes were relatively close compared to many other composers they lived during different musical times and significantly influenced those styles.
Bach's career is best known for his sacred and secular work. His work is considered to encompass all of the Baroque style. While Bach did not introduce any new musical ideas to the Baroque period his work did embrace all that was the Baroque style, though some of his choices can be considered extreme. For example his notation of the complete melodic line, including all flourishes, performers during the Baroque period were presented with the base of the melody and included their own flourishes (Wolffe, C. 381-389). Beethoven music was considered to be extremely important for the transition from the classical to romantic style. His work can be separated into three periods; early (classical period), middle (Heroic period) and late (Romantic period) (Kerman, J., 89-92).
Both composers composed many religious works but their utilization of religion and music differs. Much of Bach's work is written for the church or based on religion and he closely tied is music and text. A few examples of this are his motifs in the cantata Gottes Zeit ist die allerbeste Zeit. The slow repeating notes in the start of the piece Jesus' slow, labored walk as we carried the cross. He also uses many octave leaps, which represent the relationship between heaven and earth. There is also symbolism in his work that is not directly related to the performance. The variation in instrumentation and vocal parts during Lobet Gott in seinen Reichen of St. Matthew's Passion can be seen by some as to form a cross (Wolff, C., 298-303).
Beethoven also wrote many religious pieces but his attachment to the church is somewhat less intense than Bach's. Beethoven's religious beliefs are highly debated and though he was raised a roman catholic. While he wrote pieces for the catholic church, the Mass in C and Missa Solemnis being the most famous. The Missa Solemnis was composed in compliance with the standard Musical Catholic Mass. Some of his other work, most notably the ninth symphony contained refers to God and also mythological stories, he refers to the "Elysium" fields (Forbes, E., 880-929).
The contribution of Beethoven's works that are considered to be a transition between the classical and romantic styles is his middle or romantic period. His heroic works, which include The Eroica, Third, Fourth, Fifth, Sixth, Seventh and Eight Symphonies, String quartets 7-11, the Waldstein and Appasionata piano sonatas, and the opera Fidelio, are considered to have extended to scope of classical music. Much of his early period work was based or influenced from Mozart and Hadyn. His middle period work where hugely demanding on the performers. At the time the playing levels of musicians were not consistent as most musical endeavors were sponsored or funded by private individuals. Large symphony orchestras like the New York Philharmonic that play together constantly had not been formed yet.
Bach's music did not cause a change in musical styles. Instead his work encompassed much of the Baroque style by bringing his music to a new level. He is noted for his use of contrapuntal technique (the relationship between two or more voices that are independent in rhyme and contour but have harmonic association), his harmonic and melodic structure from a small to large scale, and his incorporation