unparallleled versus unprecedented

I am looking up these two words and they seem to have the same meaning. I thought that they mean same.Reading one of each definitions of these below, I undestood they meant same.

• unparalleled - bigger, better, or worse than anything else
  Longman Dictionary of Contemporary English | LDOCE

• unprecedented - never having happened before, or never having happened so much
  Longman Dictionary of Contemporary English | LDOCE

But (some) people tell me that they don't mean the same. I don't know how to see the words to make myself understand that they mean different. From what perspective can I also see that they mean different? For me, they are the same like these two sentences below mean the same.

1. This is more exciting than any other thing that I have experienced.

2. I have never felt this excited.

Both sentences end up meaning "This is the most exciting thing.", right? Any obvious answer or comment is helpful.

The two words do not mean the same thing.

If something that happens has never happened before, but is not bigger, better or worse than anything else, then it is "unprecedented". It is not "unparalleled".

For example a dead heat in some competition may be "unprecedented" in that it has never happened before, but it is not "unparalleled", because it is not bigger or better or worse.

Most people would also not use "unprecedented" for an unusual event that has happened before, but only on a smaller scale. They would use "unparalleled". For example a large protest might be "unparalleled" because it is the largest protest that has ever been seen, but not "unprecedented" because protests of the same form have happened before. There is some overlap because it would be normal to say "the level of protest is unprecedented" but not "the protest is unprecedented".