The anime series is a lot more subdued and atmospheric than the OVA. Partly this was because of the apparently limited animation budget and partly because of the score, but also it was because of a quite interesting shift in the perspective. Seras is the central character of the original anime, rather than Alucard, and the process of her becoming a vampire is the main plot thread. It all goes to shit in the second half though, because whoever continued the story had not grokked the style of Hellsing at all, and fucked everything up (from character design onwards). Although following the manga point by point is good the beginning of the manga is a bit rushed in terms of exposition. Style and atmosphere are basically the whole point of Hellsing though; it's all about the sheer 'rule of cool' factor, and it's unique feel and recurrent, almost fetishistic visual themes (eyes concealed behind reflective glasses, white gloves, etc.).
Thing is, with Hellsing, unlike any other anime/manga franchise, I am a complete fanboy. I own every single Hellsing related thing that exists: OSTs on CD, all issues of the manga, all DVDs. I've even read Dawn, for fucks sake. As I said, I got into Hellsing way way back in 2002, downloading fanlations of the original anime off of Kazaa. I've cosplayed as Father Anderson, made AMVs, written fan-fiction, the works (all of this back when I was 14-15). It can't really do any wrong in my mind; but I will admit, I notice its flaws and quirks whenever I intriduce people to it. I wil say, with the plot, you shouldn't really judge until you get into at least Manga/OVA 5/6. Kouta Hirano wasn't expecting the series to be popular or successful and it evolved a lot. Once Das Millenium get on the scene it picks up a lot.