The most marked likeness between the two stories is the rational approach the men take to their new environment. Otto the scientist provides the scientific background to explain what is going on at the center of the earth. Axel, in the chapters involving the volcano that spews them back to the surface of the earth, is most concerned with the workings of his compass, which seems to have gone crazy.
Crusoe's main and urgent concern is survival. He heads back to his capsized ship to retrieve supplies. In the chapter on the volcano, Axel too is primarily concerned with survival; in his case, he needs to survive the volcanic eruption that will hurl his companions and him to Italy.
The books are very much alike in their attempts to frame extraordinary events within the context of a realistic universe. Axel and Crusoe are not going to be saved by fairies or supernatural creatures. They both need to use their logic and commonsense. Both are in a "new world," but it is one that adheres minutely to the physical laws of the universe.
Both men experience a similar fear of death in the new environment. Crusoe reflects:
I had a dismal prospect of my condition; for as I was not cast away upon that island without being driven, as is said, by a violent storm, quite out of the course of our intended voyage, and a great way, viz. some hundreds of leagues, out of the ordinary course of the trade of mankind, I had great reason to consider it as a determination of Heaven, that in this desolate place, and in this desolate manner, I should end my life. The tears would run plentifully down my face when I made these reflections.
As he encounters the volcano, Axel thinks:
The mineral crust was about to burst, the heavy granite masses were about to rejoin, the fissure was about to close, the void was about to be filled up, and we poor atoms to be crushed in its awful embrace!
"Uncle, Uncle!" I cried, "we are wholly, irretrievably lost!"
Yet, in both cases, approaching the situation rationally provides the answer—and logical thinking rules both men. Axel is preoccupied with determining what part of the earth they are under, and he thinks it is Iceland. Crusoe's mind is riveted on his survival through gaining supplies and finding a safe place to sleep.
Despite the life-threatening dangers, both men also take the time out to experience the pleasure of their new environments. In Crusoe's case, it comes years later from the way he has mastered his environment and become the lord of his own domain:
At the end of this march I came to an opening where the country seemed to descend to the west; and a little spring of fresh water, which issued out of the side of the hill by me, ran the other way, that is, due east; and the country appeared so fresh, so green, so flourishing, everything being in a constant verdure or flourish of spring that it looked like a planted garden. I descended a little on the side of that delicious vale, surveying it with a secret kind of pleasure, though mixed with my other afflicting thoughts, to think that this was all my own; that I was king and lord of all this country indefensibly, and had a right of possession; and if I could convey it, I might have it in inheritance as completely as any lord of a manor in England.
In chapter 27 (in my text, the volcano episode is chapter 42), Axel experiences a deep sense of wonder and awe at the landscape and, like Crusoe, also experiences solitude. Crusoe is all alone through much of the book, while Axel has his companions, but both are in places that seem solitary and untouched. Axel thinks as he looks at the Central Sea:
I looked round a bay formed by projections of vast granitic rocks. At the extreme end was a little port protected by huge pyramids of stones. A brig and three or four schooners might have lain there with perfect ease. So natural did it seem, that every minute my imagination induced me to expect a vessel coming out under all sail and making for the open sea under the influence of a warm southerly breeze.
But the fantastic illusion never lasted more than a minute. We were the only living creatures in this subterranean world!
I hope this helps. I would focus on the idea that both stories have a very strong grounding in reason, rationality, and realism, despite the extraordinary circumstances they describe. The main characters deal with life logically. We are drawn to both stories because they seem realistic.