Dr. Van Helsing is a wonderful character... but that aside, he would stand no chance against Alucard. While Van Helsing has widsom and courage, in his day (or rather, his fictional universe) vampires are confined to the night, and contained by the goodness of God. Since Alucard is well beyond these Vampiric limitations (and ALL limitations, basically) Van Helsing wouldn't be able to win against Alucard. Van Helsing is in fact a very old man, a world renowned scientist, doctor, teacher, and philosopher (he also I think pioneered in understanding of the workings of the human brain, according to Stoker) he is very brilliant, open minded, strong-willed and wise, but very physically weak and while he could win in a confrontation with Dracula if he where restrained by the light of day, but even with his Vampire fighting knowledge and relics, he wouldn't be able to win against Dracula during the night time, or rather he may by using his relics and understanding, but he could never win in a direct battle against Dracula.
As for the Van Helsing in the movie - I haven't seen the movie so I don't know, but I've heard that this Van Helsing is actually the angel Gabriel that is killing monsters. (Interestingly enough, the first thing I thought of when my friend told me that this Van Helsing has lived for ages was that he's a vampire, and Dr. Van Helsing in the book makes a very interesting comment about if a being with the immense powers that Dracula had had come from God and not the Devil, that it could do so much good. So maybe this movie is actually based on this idea from the book! I admit that would be quite cool, and it would justify the movie's namesake, even though I hear it isn't the most substance based movie.) Anyway back to the movie, if it's not a refference to Van Helsing's comment in the book, then I think they just used that name because he was a hunter of the evil beings that plague Earth. But I'd have to see the movie to know, I heard that Dracula's story involves him being defeated and then begging the devil for a second chance? Well he'd have to have been defeated by someone, and if it was indeed the group containing Van Helsing that killed Dracula, that could send us some clues. But now I'm just rambling incoherently since I haven't even seen the movie.
One thing that I doubt is true but would be excellently cool is if this powerful vampire hunter simply took on the name of Van Helsing as a refference/homage/tribute/symbol/honor to the ancient Van Helsing who helped to end Dracula.
About the misconception about Van Helsing killing Dracula, I think it definetly precedes the Van Helsing movie, because I recall it being brought up in discussions about Hellsing's name.
I definetly agree that the misconception most likely came from "Van Helsing is a vampire hunter that goes after Dracula." and similar statements. I think people (myself included) jump to conclusions when they hear that Van Helsing goes after Dracula and assume that Dracula was killed by Van Helsing.
Look at all my trials and tribulations
Sinking in a gentle pool of wine.
Don't disturb me now, I can see the answers
'Till this evening is this morning, life is fine.