On a 1 on 1 basis, Green Arrow should win easily since Parasite only becomes more of a threat if he has meta-humans around to steal powers from. Since Oliver Queen is just a regular guy in good condition, there’s not much Parasite can use from him, unless he can now steal skills like Green Arrow’s archery skills.
Pretty poor backstory here for Parasite.
From – Green Arrow Vol. 6 #42
He also can steal energy from people by touch so even normal people are challenged.