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Well since Alucard has experience with mental powers and has great mental powers of his own it's debatable whether Aizen's illusion power would work on him, and if it didn't I don't really see any way for Aizen to hurt him.

So I would give this to Alucard 6/10.

Yes but Alucard has taken attacks designed to kill undead before and they have done nothing to him.

Okay lets go through what we do know about Aizen:
1. He is a shinigami and hundreds of years old so both of them have about equal battle experience.
2. He isn't an unholy creature so the special types of bullets wouldn't affect him.
He has a spirit pressure that can flatten other lesser creatures, therefore meaning that all the little spirits alucard conjures up would be rendered useless.
-Also in bleach there are plenty of spirit binding spells, so since Aizen has access to all the highest level ones he should be able to use one sufficienty powerful to bind Alucard. After all if a human in the hellsing family can do it I would argue that as the most powerful spellcaster in bleach he should be able to bind Alucard
-Finally he is almost impossible to hurt since he can stop punches by creatures the size of skyscrapers with his bare hands, and he also stopped fully upgraded bankai soulslayers with his bare hands, so the bullets would probably just bounce off.

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you are not thinking of the right technique. I am refering to the technique which a white cloth surrounds them in a whirlwind and then teleports them to another location. I am fully aware of the fact that the step movement utilized by Byakuya and other powerful shinigami is not teleportation.
Secondly I have read the entire manga of Hellsing up to about ch. 73 and I have never seen Alucard display any teleportation abilities.

I can pull out all my volumes right now and reference teleportation.

- Volume 2, Order 6, Balance of Power part 2: Integra and Walter head to Art Museum alone. Shortly after Enrico insults Integra, Alucard appears seemingly out of thin air behind his Master.

-Volume 3, Order 3, Elevator Action Part 2: After the Brazil SWAT team had busted into the suite, they found the entire place empty, shortly stumbling on Alucard's coffin. As soon as they go to touch it Alucard appears seemingly out of Nowhere.

-Volume 4, Order 1, Elevator Action part 6: While fighting Alhambra Tublacain, who like a normal vampire with superhuman sensory abilties, his two decoys along with him self appeared suddenly in three different positions around Alhambra, catching him completely off guard each time.

-Volume 5, Order 3, D part 5: While Integra and Walter are discussing options to get Alucard onto the HMS Eagle, Alucard rises up from Integra's shadow, appearing from nowhere.

-Volume 5, Order 5, D part 7: In the three panels on the last page of this Order, the last two are the exact same portion of damaged deck of the HMS Eagle. In the second it is bare of nothing but smoke, shrapnel and debris. In the next panel Alucard's boots are seen where they had not been.

Unlike Bleach, Hellsing is more...how would I put it....Mature. Its characters don't have names for their attacks like younger demographic manga. Alucard would most likely use his taloned, indestructible hands to tear Aizen to pieces, if not just become an amorphous blob and devour Aizen.