I haven't seen a lot of Star Trek: Voyager episodes, but I know of at least one episode (Scorpion, and there might be more) where Janeway and Chakotay get into an argument about a decision to make.  Both of them have different opinions about a course of action, and both have very good reasons for their beliefs.  In the end, though, it seems like Janeway has an attitude of "I'm the captain, so I'm always right.  Since you are a dear, dear friend of mine, I want you to agree with me unconditionally.  We're doing this my way."  Of course that's not her attitude, but I sometimes thought that she didn't value Chakotay's advice.

Anyways, is there an episode where they have such a conflict and after a while Janeway realises that Chakotay is the wiser one in that particular instance?  Similar to Star Trek: First Contact when Captain Picard had a fight with Lily and then discovered how right she truly was that he should self-destruct the Enterprise

In the earlier episodes I didn't feel that she didn't value Chakotay's opinion, but she had to establish that it was a federation ship, not a Maquee ship and things had to run a certain way.  She also had to establish the she was the Captain, and order had to be kept.

Agreed.  And later on, in an episode like Scorpion, Chakotay knew this all too well. 

Considering that a first officer is meant to help the captain, I was still hoping that there was even one episode where Chakotay was the one who made the right decision

I've seen most of them and...honestly I haven't noticed this
Mainly because whenever they talk I'm distracted by Chakotay's bad acting ( don't get angry, the actor has admitted to playing the part badly because he didn't like his character ).
Now that I think about it though, I have noticed this, and I don't remember any episodes where he is right and she isn't, but I'm sure there are one or two like Art said.

Ahh, very nice. Had a chance to watch more of the series?