i think exquisite is only for objects. beautiful is for both people and objects!! ciao,fede

Other possible definitions (one of which is mention by mike1988) are: -pleasing through beauty, fitness, or perfection <an exquisite white blossom> -acute , intense <exquisite pain> -having uncommon or esoteric appeal I think, that given these possible definitions, you could use exquisite in connection to a person. However, I would more often associate with an object or some attribute of a person ("Her hair is exquisite").

'exquisite means extremly beautiful or carefully made. Also in a formal way - strongly felt, delicate and sensitive. The room was decorated in exquisite taste. an exquisite sense od timing

Yes, as Fede said , you can use them both to describe people and objects, eg an exquisite and beautiful piece of jewellery and the woman's face was a delight to behold, exquisite and beautiful.