The African Queen came out in 1951, which puts it right in the middle of Hollywood's historical timeline. It's not from the heyday of the studio system, but it also predates the auteur revolution that followed a generation later. As such, it's kind of an odd duck; it doesn't quite have the "classic" feel that a stylized black and white movie might have, but it also doesn't feel modern at all.
Certain aspects of the movie stand out as timeless. Even today you can pick up on Humphrey Bogart's charisma, and Katherine Hepburn is very good at being Katherine Hepburn. Furthermore, the script is well paced, giving the viewer a clear sense of how far down the river the boat the African Queen has traveled, and thus how close they are getting to the German boat the Queen Louisa, which they plan on sinking. That style of movie star performance might not be typical anymore, and the script makes some choices that would be out of vogue today, but that doesn't necessarily diminish their appeal.
In many other ways, however, the African Queen feels very dated. For one, the film is mostly a romance between Rosie, a missionary played by Hepburn, and Charlie, a boat captain played by Bogart. Their relationship is defined by the fact that it's just the two of them on the boat, and their close quarters cause them to alternate between sparring and falling in love. But their romance is unbelievably chaste to modern eyes: Rosie's undergarments go from her shoulders to her mid-thighs, so even when she's bathing in the river there's nothing remotely revealing. While there is a scene where Bogart's resting his head on her lap, they barely have any physical contact. I'm not noting their lack of intimacy for prurient reasons; it's relevant because removing sex from their relationship changes where the tension in the story is. The question behind their flirtation is not whether or not they will end up together, it's whether or not Rosie can convince Charlie to blow up his boat by ramming it into a warship. I don't think I've ever seen a modern romance where sex wasn't the point; the tameness of their interaction definitely feels old fashioned.
Also, Bogart is so far away from a modern star that it's remarkable. There is a scene where he has to pull the boat through a shallow part of the river, and when he comes back onto the boat he's covered in leeches. When he takes off his shirt to get the leeches off I almost gasped because he looks like a human being. The African Queen is in large part an adventure story, and most of the people who are cast in modern adventure stories have followed in Arnold Schwarzenegger's steps and built up their bodies so they look more like gods than men. Bogart had a tiny frame that he clearly hadn't developed; it isn't that he looked bad or that he looked scrawny, it's that it's so rare to see someone in a movie who isn't totally jacked that it took me by surprise. He had a mental toughness, instead of mere physical strength, and that's another thing that we rarely see anymore.
Perhaps the ultimate way that this film is caught in between eras is that it's a film set in Africa with the word Africa in the title, and yet, the only speaking roles in the movie belong to white people. On some level that makes sense; the story is claustrophobic, since it is about two people trapped on a boat, so the fact that the story focuses on Caucasians isn't automatically offensive. At the same time, you would have to think that if this was made in a post civil rights era there would be a bit more of an effort to broaden the focus towards the people that live there instead of just focusing on the tourists. But it's also good that this wasn't made any earlier than 1951, because if it had been, it definitively would have had a few scenes that were actively objectionable.
It can be hard to look at films that are this old with fresh eyes. (Or ears, for that matter; the way the score remained jaunty instead of becoming dynamic when the boat was perilously close to crashing in white water rapids was another choice that seemed out date.) If you can enter the African Queen's world with an unbiased mind, you can find an engaging tale enacted by some of the best old school stars. If you can't, you'll find a romance that doesn't go beyond modest flirting and an adventure movie where they could turn around and stop adventuring at any point. Maybe your best hope is to see it with a partner on a boat, that way you can spend the rest of your time arguing for and against it while falling in love.