Then this fight is gonna be harder to decide then I thought.
For the first 2 rounds, I think Jack's gonna have an advantage in weaponry, strategy and technique, maybe, and him using a sword is probably giving him advantage in a fight against pistols, but Alucard, as mentioned, has Type 1,3(& 7) immortality and holy weapons don't hurt him as much comparing to other monsters, and I don't really think Jack can 'kill him' or perform BFR so...(I'm not sure)...it's also worth mentioning that Alucard is kinda intelligent and skilled in weaponry too, considering his fighting experience. As a result, imma just say that they'll end up in a tie (or in a really long fight until one of them runs out of stamina or Alucard Actually dies due to attacks by Jack's holy sword).
The last round tho, is even harder to determine. Undoubtedly, Alucard in Type 0 is insane, but Jack, being able to hurt Aku, is no joke either. Something worth mentioning is that Alucard can now have (an army of) assistance and can use his sword(s). I 'assume' Jack is more skilled in swords, but again Alucard's fighting/past experience makes him kinda skilled too.(well this point doesn't prove/change anything my bad) Other than that, the factors are pretty much the same. This round's probably end up in a tie like the previous 2 rounds, but the whole porcess's gonna get an incredibly large area destroyed and the result's gonna come out sooner.
Both Alucard and Jack are awesome and incredibly strong characters, it seems that the only way to find out the true winner is to actually let them fight (wtf am I saying). Anyway, these are just my opinion/analysis/(whatever), sorry I don't know much about Jack and how this website works, so there'll probably be mistakes, so please do let me know if I'm wrong or something like that. Thanks.