Age range is similar: both are applied to young men.
Style is different, and both of them are stylistically marked.
юноша is commonly met in classic literature. Also in educated speach. Also some of my school teachers used it:) I have an impression that most of people using it are aware of this slightly literary scent, and use it by mood. There is a joking for "вьюноша":)))
I think, a young person is unlikely to refer to a person of the smae age as юноша - unless he plays with style.
парень is very common. Often used by young people to refer to other young people. By adults as well.
It is used in literary language, of course - but it sounds simple and familiar. I don't think they would use it in a formal text, e.g. biology textbook.
you CAN combine парень with молодой: "молодой парень" to emphasise youth. Eg. : "you, a молодой парень, spend hours on Italki instead of courting girls! WHy?". Парень is just a noun.
you can NOT combine юноша with молодой - it sounds stupid as юноша clearly means 'somebody young' (юный).
adj. юный - is now a poetical way to refer to 'young'. It affects our perception of юноша.
As Anna (rahter brilliantly!) suggested, "мой (её) парень" is 'my boyfriend (her boyfriend).
I suspect, юноша belonged in past to educated speach, and could be influenced by Slavonic.
While парень smells as somethat that 100 years ago could be regional colloquial (or even village) speech.