The Captain's final entry has finally arrived, and it has a fair bit in common with Jonathan's final entry/more generally several of his earlier entries. I've just been having fun kind of mentally collecting them, so here's what I have specifically noticed...
First off, I already wrote a post about a couple earlier similarities in how they both write to keep a clear record when strange things are happening, and how they both indulge the superstition of others (only to later realize the truth of it). So there's that. But then there's a bunch more recent stuff as well.
I am beginning to feel this nocturnal existence tell on me. It is destroying my nerve.
Jonathan, 12 May
Still fog, which the sunrise cannot pierce. I know there is sunrise because I am a sailor, why else I know not.
Captain, 4 August
One of the first things Dracula does with Jonathan is keep him up all night to get him on a nocturnal schedule. While Jonathan eventually spends more time awake during the day when he knows Dracula is weakest, it seems like Dracula kept up their late-night talks until almost the end, meaning that every time he did so it came at the cost of losing some sleep. Even when he does get to sleep, there are some hints that he often has nightmares. (I'm not adding any sleeping quotes here because the points go together, and there would be so many to collect.)
With the Captain, one of Dracula's earliest/most persistent methods of torment is to deprive the crew of their sleep. The storms, if you believe he summoned them, start pretty early. Even if you don't buy that though, their fear leading to double watch even as more and more of them disappear leads to less rest. And then when the Captain is able to rest well he's awakened to find even more death. Eventually, Dracula deprives him of sunlight too, by surrounding the ship in a fog so thick that it's hard to even tell when it is day or night.
I am alone in the castle with those awful women.
Jonathan, 30 June
While the Captain doesn't have any such clear quote, it is very much a major detail that he is entirely alone with Dracula at the end. In a sense, this is a contrast, because Dracula being gone is what makes Jonathan talk about being alone with such fear, but the essentials of the situation are the same: they're trapped in a place they cannot leave, with only vampire(s) for company who want to kill them - there's even an extra parallel if you add in the person they both feared/relied on has recently left (not that the first mate and Dracula fill the same role, but in this specific way it's kind of an echo).
I have placed the crucifix over the head of my bed—I imagine that my rest is thus freer from dreams; and there it shall remain.
Jonathan, 12 May
I shall tie my hands to the wheel when my strength begins to fail, and along with them I shall tie that which He—It!—dare not touch; and then, come good wind or foul, I shall save my soul, and my honour as a captain.
Captain, 4 August
They both rely on a crucifix to protect them from Dracula... at least in a limited capacity. Jonathan has seen its efficacy proven, while the Captain more just has faith in it driving off demonic beings like Dracula must be. There's kind of a neat contrast in their opinion of the crucifix itself in that way, with Jonathan initially dismissing it as idolatrous but somewhat reevaluating his own faith once seeing that it affects Dracula, while the Captain at one point fears that he's been abandoned by God but later finds refuge in holding on to his own faith, with the crucifix itself serving as a physical manifestation of that.
And then away for home! away to the quickest and nearest train! away from this cursed spot, from this cursed land, where the devil and his children still walk with earthly feet!
Jonathan, 30 June
Jonathan finally decides to risk it all to flee for home, finishing his original round trip. The Captain lashes himself to the helm so that nothing can stop him from completing his journey to the best of his ability. Both their final acts of defiance are in an effort to try and reach other people, to defy being trapped alone with these monsters.
If this book should ever reach Mina before I do, let it bring my good-bye.
Jonathan, 4 May
At least God's mercy is better than that of these monsters, and the precipice is steep and high. At its foot a man may sleep—as a man. Good-bye, all! Mina!
Jonathan, 30 June
If we are wrecked, mayhap this bottle may be found, and those who find it may understand;
Captain, 4 August
Both Jonathan and the Captain realize that there is every chance they will not survive their journey/live beyond their final entry. Jonathan verbalizes the possibility of his death much earlier and more often, but in the end both of them write their final lines with the hope of an outside audience who can learn from their experience and understand why they did what they did. They also both choose to face a likely death. (Jonathan's choice to flee at all costs is maybe closer to the mate's choice to escape into the sea than the captain's decision to stay, but in both cases they hope to preserve their words even after their own death.)
This was the being I was helping to transfer to London, where, perhaps, for centuries to come he might, amongst its teeming millions, satiate his lust for blood, and create a new and ever-widening circle of semi-demons to batten on the helpless. The very thought drove me mad. A terrible desire came upon me to rid the world of such a monster.
Jonathan, 30 June
But I am captain, and I must not leave my ship. [...] ... well, then all men shall know that I have been true to my trust. God and the Blessed Virgin and the saints help a poor ignorant soul trying to do his duty....
Captain, 4 August
Both Jonathan and the Captain act at least partially out of a sense of duty. Jonathan early on is determined to do his duty by Mr. Hawkins; on his final day in the castle, he feels a responsibility to try and stop Dracula from going to London. Sure, it's mixed in with his own hatred and (wild) desire for revenge, but at least part of the reason he attacks Dracula with a shovel is because he doesn't want to be a part of getting him what he wants. He doesn't want to help transfer him to London.
The Captain, ironically, chooses to hold fast to try and transfer his cargo to England. Or at least, he feels loyal to his responsibilities and duties as a captain. He's failed in protecting his crew, and he will probably fail in completing his journey/protecting his ship as well, but he is determined to try his best until the very end. And I think part of this determination is the same kind of refusal to capitulate to Dracula that Jonathan shows on Shovel Day. As readers, we know it would be better if the Captain intentionally scuttled his ship... but from the Captain's perspective, everything that has happened so far has been detrimental to him completing his trip. The storms, the crew being picked off, the fog getting him lost when he nears shore... as far as he knows, it may well seem like the monster on board doesn't want him to reach land. And so his effort to do just that is just as much in stubborn defiance of Dracula's will (as he perceives it) as Jonathan's attempted attack was.