Hi Niwantha,
they both mean "Tenacity" but
"Persistance" has a more negative or neutral connotaction than "Perseverance".
"Persistent" means stubborn/obstinate. For example: "A man who persistently invites a woman for dinner when she doesn't show any interest in him" may be annoying for the woman. He is persistent accordindg to the woman.
The man, on the other hand, may fell perseverant (brave) in reaching his goal because he is really in love with her.
So it really depends on how you look at the things. You can give to someone's tenacy a positive o negative connotation.