A lot of people that I have met affirm that the KJV is the only reliable
translation, but I had heard somewhere that the text for the NASB actually dates back BEFORE the KJV therefore being closer to the original
manuscripts.
Which group is right?
Unfortunately no translation is perfect no matter how old it is. The best thing to do is to read it in the original languages. Also, there is a story to every translation such as which manuscript or combination of manuscripts the translators chose, the interpretations used in the translation, and even the culture of the times. That's partly why we need new revisions as interpretations become clearer and as language evolves. But no matter how they do it, a lot of meaning is lost in translation.
For example, after I learned Greek, going from Greek to English in the New Testament is like going from a 3-D picture to a 2-D picture. A small example is the word "life." In Greek there are 3 words for life (bios for physical life, psuche for the psychological life, and zoe for the life of God; you can find the Greek spelling elsewhere) while in English we only have one word, life. Some translations, however, do not tell you which life the verse is actually talking about. The KJV I have translates Luke 17:33 as:
Whosoever shall seek to save his life shall lose it; and whosoever shall lose his life shall preserve it.
What is the life here? The Greek says psuche, the psychological life or the life of the soul. So that, at least for me, changes the way I look at this verse. So it doesn't mean that we give up our physical life necessarily but the life of our sol which is deeper.
The NASB I have is a bit better which translates the verse as:
Whoever seeks to keep his life will lose it, and whoever loses his life will preserve it.
Then the NASB has a note saying that "life" can also be translated as "soul." The newer KJV may have something similar.
Though I do have my favorites, I would never say such and such a translation is the most reliable because they all have their faults.