I know that this has been done before, and the majority of people on that thread favored Percy as a winner, however, due to lack of information in it's OP, I thought I'd make a more detailed Battle, see how it goes.
-Current versions of characters. Percy as seen at the end of "The Mark of Athena", Harry as seen at the end of "The Deathly Hallows", but prior to the 19 year timeskip.
-No outside help unless stated in scenario
-No outside weapons unless stated in the scenario
ROUND ONE: The Day a demigod and a wizard shopped til they dropped.
-Morals on for both
-Harry gets his Phoenix core wand
-Percy gets Riptide (which will indeed hurt Harry in this instance)
-No other weapons allowed.
-Fight takes place in their local Wal Mart (It is vacant)
-Fighters start on the opposite ends of the store from one another.
-Both know of each other's abilities as well as what they are (Wizard/ Demigod)
ROUND TWO- Things get serious
-Both are willing to kill the other
-Both have their normal abilities
-Harry gets the Elder Wand, the Sword of Gryfindor and is riding on the back of Buckbeak the Hippogriff
-Percy gets Riptide and is riding on the back of Blackjack the Pegasus
-Win by k.o, Death, BFR or incapacitiation.