na-adjective
Describes a person, behavior, or appearance that is overly showy or pretentious, often with a negative connotation.
彼の虚飾的な態度が周囲の反感を買った。
His ostentatious attitude rubbed people the wrong way.
あのレストランの内装は虚飾的
The interior of that restaurant is so showy that it's hard to relax.
見栄っ張り is a noun/adjectival noun describing a person who is vain or showy, focusing on the person's character, whereas 虚飾的 describes the quality of being ostentatious in appearance or behavior.
Compound of 虚飾 (kyoshoku, 'ostentation, false adornment') and the adjectival suffix 的 (teki, '-like, -tic'). The exact historical derivation is uncertain, but the word follows a common pattern for forming adjectival nouns from Sino-Japanese nouns.