To be fair, I've only seen the first four episodes of Hellsing Ultimate, but I think the beginning stuff that both series covers is done much better in the TV series, and I don't see how this can be disputed because the whole first episode of Ultimate is incredibly rushed and just whizzes past everything; yet the fourth episode is incredibly redundant, drags things out to seemingly no end, and is just a gigantic waste of the 45 minutes it was given to tell and show something. Everything covered in it could've maybe been done in 25 minutes, leave the rest of the time for something more interesting. The TV show never once bored me like that.
I also don't think the humor is incorporated/executed very well in the OVA series, even though it tries to follow the style and art of the manga. The TV series pretty much left that out (save for the awesome "spirit of Harkonnen" shorts at the end of every episode), and for good reason.
The animation and art in the OVA series are pretty, sure, but there's something about the TV series that strikes me as having more craft even though the funds are limited and the animation isn't always the greatest. Better drawings and use of color, I think. It's probably accurate to say, however, that the OVA series is drawn more closely to how Kouta Hirano draws.