The show transcript on BuffyWorld notes that Prince of Lies was old and slighty paunchy, both of which would have contributed to his poor fighting skills against a vampire in top condition like Angel.
Nostroyev is wearing a luxurious costume resembling late 19th century European aristocratic fashion. He's got a pointed beard and a substantial beer belly. The Prince of Lies is a bald, creepy-looking pale vampire—clearly very old as his pointed ears, odd teeth and bony fingers demonstrate. He stands hunched over and holds his long-fingernailed hands together in front of him.
He seems to have been taken entirely by surprise by Angel's attack.
Angel steps back, seemingly allowing Nostroyev to pass, but punches him in the stomach instead. Angel grabs the axe out of Nostroyev's hands, punching him in the stomach with the handle, breaking it. Angel thrusts the splintered wooden handle through Nostroyev's chest, causing Nostroyev to scream and turn into dust.