They seem to mean the same thing, but I've seen 有意思 quite a few times in my books, and never 有趣. When is 有趣 used and why (especially in comparison with 有意思)?
Mostly,有趣 means something or someone is really funny. 比如,他是一个有趣的人(He is a funny man.) 你有什么有趣的故事分享吗?(Do you have any funny story to share?)
And,有意思,some time means the same meaning of 有趣 as something is attractive. 比如,这个游戏很有意思(The game is very interesting).You can also say 这个游戏很有趣.
But when someone use 你这样有意思吗? (Do you think it's appropriate to do[be] that?) Here 有意思 means "it's not appropriate". Or 真他妈有意思! (It's f***ing funny, HaHa!) Here 有意思 means "someone ro something give me sh**".
When people say 有意思, you should tell the context and tone.
有趣 - fun 有意思 - interesting
To break the vocabulary literally, we have 有/趣 and 有/意思. The word 有 carries the meaning similar to "there is something" or "it has something". 趣 can be interpreted as "fun". 意思 can be translated to "meaning".
So, these two vocabularies can be broken down literally as:
X有趣 - there is fun in X / X is fun X有意思 - X is interesting
In many conditions, they have same meaning.
这个人真是有意思 This in many conditions means this people makes you unhappy.
这个人真有趣 This is normally express someone is funny.
To me these two words don't differ too much. Maybe the only thing is 有意思 seems a little little little casual.
有趣 means it is something makes your happy. 有意思 means it is something meaningful.
Actually, it is quite depending on the whole sentence or even the paragraph.