You could use both interchangeably to mean 'he is sitting across from me at the same table' and it would be fine, but technically they are slightly different. He sat across the table from me. This means just that he's sat at the same table, opposite you. He sat across from me at the table. This can mean the same thing as above, but can also mean that you may not be sitting at the same table. You could be sitting at a bar and he is sitting across from you at a table that is there. Most of the time though people will just think you're saying you're both sat at the same table no matter which one you use.

Hi Sean, They seem to say the same thing! Keep on learning! Regards, David