这两个形容词都可表示价格、价值高。“昂贵”更加书面，可用于抽象意义，而“贵”比较口语化。
Both adjectives mean “of a high price or value ". The former is more formal and can be used in an abstract sense, whereas the latter is more colloquial and refers to a concrete price.

1.用于一般商品时，因为“昂贵”是双音节词，可直接与“价格”等搭配，“贵”则常和“很”等搭配。
When applied to merchandise, 昂贵 is used with 价格 while 贵 is usually used with 很. For example:
（1）这场演唱会入场券的价格很昂贵。
（2）这场演唱会入场券的价格很贵。
“贵重”常用于贵重物品，如“昂贵的珠宝”、“那件古董十分昂贵”等。“贵”则可用于多种物品。
昂贵 is often applied to valuables, e.g. 昂贵的珠宝, 那件古董十分昂贵. etc., while 贵 is applied to all sorts of things - valuable or not.

2.用于抽象意义时，常用“昂贵”。
昂贵 is usually used in an abstract sense.
（4）为了赢得这些客户，企业付出了昂贵的代价。

3.“贵”还有一些其他意义，表示可贵：“贵在坚持”等；还有用作敬语：“您贵姓？”和“贵国”等。
贵 also has several other meaning and usage, e.g. 贵在坚持；it can be used as "a term of respect", e.g. 您贵姓？贵国 etc.