Hola, As Seaira-san already said, 大変申し訳ございません is politer than 大変申し訳ありません though both are polite ways of "I'm so sorry". (In general, we say 申し訳ございません to clients.) We have varios ways of apologizing and in this case, it's for the verb ある. It's negative form is ない and the level of politeness is: ない --> ないです --> ありません --> ございません Espero que entiendas.

Thank you for your explanation! Saeira-san I can see how important being polite in Japan is.

申し訳ございません I believe this is the more polite version that makes you sound more sorry when you do something troubling. 申し訳ありません This is still a polite version but is less formal or sorry than the above. It literally means I have no excuse for what has been done.