I oughta sit down and read Hellsing some time. I first saw the anime when it was new (and as a kid that was THE coolest shit in the world). I never much got into the OVAs much when they first started coming out, mainly because I vastly preferred the more serious, dramatic, and somber tone of the anime adaption, along with the royally sick music by Yasushi Ishii.
https://youtu.be/C04brWWdMgwhttps://youtu.be/h92yZAi4WLohttps://youtu.be/lPHKRzJDKK8https://youtu.be/mV08aY6XaNchttps://youtu.be/q5ODUgCCUcIhttps://youtu.be/vqEuxwZAbkAhttps://youtu.be/ciYqagz7hRUhttps://youtu.be/c0d3IAcuUxMRewatching the anime a little while back, there's a lot about it which holds up, but also some which doesn't. With what little I've taken in of the manga and the OVAs, it seems Seras is regrettably given less characterization (in some aspects anyway, it doesn't portray her struggling to hold on to her humanity in the same way), but Alucard instead seems to have a LOT more.
In the anime adaption, most of what he does is to be the unstoppable cool guy who stomps ass at every turn, which is fun for how he just sadistically relishes in it all, but can leave things to be desired in terms of stakes, the manga and OVA would go into more about his history and how he became the unstoppable horror on a leash that he is.
Part of this is of course that Hellsing got adapted pretty early on, so the anime ran out of material to adapt, hence why it goes on its own course, inventing characters like Incognito. Kouta Hirano wasn't particularly satisfied with how much it strayed even before that, so while Gonzo had aspirations to adapt more material in the future, probably where they would go more into Alucard's past, creative differences meant it wasn't in the cards. The OVA series which was made is much more faithful, but lacks some of the anime's distinct style.