They seem like they are fairly similar areas, so why did Kosovo press for independence when Vojvodina didn't?
I'm not sure what you mean by "they are fairly similar areas." They're not THAT similar...at all. The premise of your question is odd. Vojvodina has had a close historical association with Hungary, and is all the way in the Northern part of Serbia. Kosovo has had a strong historical relationship with Albania, and is in the Southern part of Serbia. There are vast cultural, historical, lingual, and religious differences between the areas.
Vojvodina was conquered by Magyars & a few Kabar tribes (after they left Khazaria) in the early 900s (maybe even the 890s). It was known as Vajdaság, & remained a part of Hungary for over six centuries until the Ottoman invasion of Eastern Europe. Hungary suffered a defeat to the Turks in 1526 at the Battle of Mohács, after which the opportunistic Serb mercenary Jovan Nenad conquered the area, and proclaimed himself emperor for a brief period, until it too was annexed by the Ottoman caliphate. In 1690 it was restored back to Hungary, which was now the "Habsburg Kingdom of Hungary" or Austria-Hungary; however, the area was settled by a large quantity of Serbs during the Great Serb Migration, when Serbs from Ottoman territories settled in the Habsburg Monarchy in 1690. Much like in present-day southern Hungary, Islam did not leave a lasting impact in the area, in so far as, current practitioners of that religion.
Kosovo in the 800s was a part of the Bulgarian empire. It was taken by the Byzantines in 1018. By the late 1100s it was taken by Serbia. In 1371 Serbia fragmented into many independent city-states, so Kosovo was independent, but controlled by a powerful Serbian family named Branković. In the early 1400s, regions of Kosovo, were part of the Principality of Dukagjini, which was incorporated into an anti-Ottoman federation of all Albanian principalities, the League of Lezhë. The were eventually defeated, so Kosovo was part of the Ottoman Empire from 1455 to 1912. During this time, Islam was introduced to the population.
Kosovo spent 450 years under Islamic rule & Islamic law, while Vojvodina spent about 150 years, and was the outer, western/northern border of the Ottoman empire (along with southern Hungary), so it remained close to the battle-front. As a result, today 95. 6% of Kosovo practice Islam to 3.7% Christianity. In Vojvodina only 0.75% continue to practice Islam today, while 87.7% are Christians (mostly Eastern Orthodox, but also a strong minority of Catholics).