There's no price difference whatsoever. By booking via the website you can (hopefully) ensure you get tickets for the popular trips, however, we also found that when on board they sometimes had extra excursions that weren't on the web site. We went in July and from the list of excursions in our cabin on day one, one of the tours we were on was fully booked which could be why extra ones were added on. I also know some people were disappointed that they couldn't get on the ones they wanted. If there are some you really want to do then I would book in advance. You can always cancel when on the ship but a charge may apply.