I agree wholeheartedly with Jessica Brown's answer, but there's another dimension to accuracy: the text a translation is based on. Before the Tyndale Bible, English translations were made from the Latin translation (the Vulgate) and not directly from the Greek. For obvious reasons, these translations are automatically less accurate to the original texts than more recent translations.
Until quite recently, English Bibles were translated from a version of the Greek New Testament called the Textus Receptus produced by Desiderius Erasmus. It was formed from just 6 Greek manuscripts and was supplemented by translations of Vulgate texts back into Greek. By contrast, modern Greek texts make use of over 5,800 Greek manuscripts including some found only within the last 100 years.
Modern translations of the Old Testament are also informed by the Dead Sea Scrolls, which strongly support the Masoretic Text. Older translations were unable to benefit from these sorts of discoveries.
Thankfully, English translators have a long tradition of including introductory notes to their work. If you look in the first few pages of a Bible, it's quite likely you will be able to read an impassioned argument for why that particular English version should be read and used. You can get a good idea of the translation philosophy represented in the subsequent pages and where the editors stood on controversial issues such as gender-inclusive language, archaic pronouns referring to God, translating the names of God, and so on.