Although were looks like a past tense, it is used in what is called the second conditional here. Grammar guides tend to ignore that fact that this conditional has a time frame. Referring to now, we say
If I were a kid, I would play with my toys now.
But referring to the past, we say
If I had been a kid ten years ago, I would have played with my toys then.
So we have to look to see what time frames the tenses in the question refer to. In
- "If I had been a kid, I would've enjoyed the movie a lot more"
both clauses are in the past as it refers to yesterday. It would, however, make just as much sense if you had seen the film ten years ago (unless you were a kid then!).
- "If I were a kid, I would've enjoyed the movie a lot more"
the first clause is a tense usually used for the present:
If I were a kid, I would go and see the film this afternoon.
So at first glance, sentence 2. has the tenses mixed, but there are two possible explanations.
Firstly, it could be referring to a fairly general sense of present which includes yesterday:
As I am not a kid, I chose not to go to the film yesterday.
This works because if I say I am not a kid, it is a reasonable assumption that I was not a kid yesterday. We can test this by trying
As I am not a kid, I chose not to go to the film in 2009.
We see that this does not work because, even if I say I am not a kid now, it does not follow that I was not a kid then. So it would be better to say
As I was not a kid in 2009, I chose not to go to the film then.
Now let us see what happens if the film in the original question were ten years ago.
If I were a kid in 2009 when I saw the film, I would've enjoyed it a lot more.
This is possible, but does not sound good. This is because were can be used as the past conditional but it is not normal. Had been is better.
So if we ignore the last option as it is not good English, then it comes down to a choice between
- If I had been a kid (yesterday, in the past)
- If I were a kid (now, which includes yesterday)
So both are valid. My preference is for 2. as 1. seems to draw an unnecessary contrast between yesterday and today, but that is only a personal preference.