If we look at the "To be or not to be" soliloquy and the following scene with Hamlet and Ophelia from PBS' Hamlet and compare it with the original text and earlier adaptations, several differences stand out.
First of all, PBS' performance is a modern performance in regards to sets and costumes. So the characters are not dressed in Victorian attire as they were in previous adaptations. They are dressed as we are dressed today. The sets are also more modern and the directors have used modern devices such as video cameras.
For example, in earlier adaptations, Hamlet was shown as suspecting Polonius and Claudius spying on him when he heard footsteps while speaking to Ophelia. This occurs before Hamlet asks Ophelia "Where's your father?" In PBS' performance, Hamlet suspects that he is being spied on due to the noise and movement of the video cameras in the hall. So the entire sets and circumstances have been updated and modernized to today's way of life.
As for the performance of Hamlet in the soliloquy, I've personally found David Tenant's performance to be more subdued, more deep, emotional and even melancholic than some other interpretations. For example, in the 1996 film Hamlet, the soliloquy is delivered with more anger and less pause by Kenneth Branagh. Please watch both of these and compare and interpret the differences in your own opinion.