What are the similarities and differences of Pentecostal Theology compared to Baptist Theology?
Being neither Baptist nor Pentecostal, I can only give you my understanding based on study of the official doctrines of those churches. I also must add that, as with most churches, the "official" doctrine may differ from that held by the average believer. For instance, some Baptist groups claim to be Calvinist in doctrine, but the average Baptist would have difficulty in believing that they may be lost even if they feel saved and do what the church tells them to do for salvation and live a good, moral life.
There are many similarities between the doctrines of the two groups. Both believe in one God and His son Jesus Christ (but more on this later). Both believe that baptism is immersion in water. Both believe that the saved will go to heaven and the unsaved will be punished in hell. There are probably a lot of other similarities shared by all or most Christians.
Pentecostals and Baptists are generally premillennialists, although some Baptists do not believe in a rapture or a 1,000 year reign of Christ on earth. Generally both believe in assembling on the first day of the week for worship, although Seventh Day Baptists believe that the Sabbath (Saturday) is binding on Christians as well as Jews.
The major differences are as follows:
Many Pentecostals believe that baptism is a prerequisite to remission of sins, while most Baptists believe that it is a requirement after forgiveness.
Many Pentecostals believe that one is not saved until he has believed, been immersed, and received the "gift of the Holy Spirit". Baptists generally believe that one is saved upon repentance and prayer, and that baptism follows. Most do not believe in a miraculous manifestation of the Holy Spirit in healings or speaking in "tongues." (I enclose that last word in quotations because the Pentecostal view of tongues differs significantly from the biblical statement of what is meant by speaking in tongues; the Bible teaches that it is the miraculous knowledge of human languages spoken by the hearers.)
Most Baptists believe in the Trinity of the Father, Son, and Holy Spirit as three "persons" in the godhead. Some Pentecostals believe that there is one member of the godhead, God the Father, and that Jesus was God shown in the flesh (but in no way separate from the Father) and the Holy Spirit is God manifested in believing, obedient people.
Most Baptists believe "once saved, always saved," regardless of how one lives afterward. Most Pentecostals hold that one may lose one's salvation by willfully returning to a sinful life.
This may be oversimplifying things, but the most distinguishing mark of Pentecostalism is probably "speaking in tongues." If there is a distinguishing mark of Baptists, most would say that it is a belief that "once saved, always saved."
I hope this is helpful to you. Again I emphasize that my knowledge of the doctrines of each of these is mostly gained from reading books by and about them, and speaking with friends who believe either doctrine.