It depends on the type of setting you change it to. The novel is a tale of adventure (the science of this work is completely off-base, as opposed to some of Verne's other works, most notable 20,000 Leagues Under the Sea), and it is pretty standard. You have the over-confident leader, with a naive/nervous follower, and a faithful companion. Put them in any dangerous setting, and the characters at least would stay the same.
In a voyage through an uncharted jungle (toward a rumored lost civilization), Professor Liedenbrock would still be the "expert" on this civilization. Axel could still be unsure of his uncle's scholarship, forced to accompany him through the jungle. Hans, the ever-silent companion, would remain helpful and indispensible. It is only the dangers along the way that would be changed. However, in a jungle the team is more "rescuable" than they would be deep within the earth's interior. They would also most likely find other human inhabitants (though there was a brief encounter with a prehistoric hunter in the original story, but with no interaction).
On a sea voyage, the conflicts would be still with nature. There would be little chance of escape in the middle of the ocean, any more than there was in the middle of the earth. The dangerous encounters would be with weather and sea creatures (and perhaps passing pirates).
Place the story in the Arctic or Antarctic, and you have conflict with weather and procurement of food. The changes in landscape would be be even more limited than in the original, unless there is a "lost civilization" on Antarctica.
In recent film adaptations, some of these elements have been added to the original story (along with the addition of female characters on the journey itself).