So I was talking to my friend (who learns Japanese outside) that I was learning Japanese on this cool website, and since I had just finished i-adj conjugations I was talking to him about it.

As you know, Season 4 lists i-adjective conjugations as:

あたらしいです

あたらしかったです

あたらしくないです

あたらしくなかったです

However, my friend told me that he learnt that i-adj should be conjugated as such:

うるさいです

うるさかったです

うるさくありません

うるさくありませんでした 

To my untrained eye, this seems like a problem of formality. In fact, I did a little research, and both are acceptable.
http://rcl.pliable.us/J-adj.html

My question is, when would you use either of these? Is the first method any less polite than the second? If so, when are each of them used?