尊い is also sometimes written as 貴い, and has two readings: とうとい and たっとい. The basic meaning of 尊い is holy or sacred. Therefore it also describes something as precious and invaluable. 大事 (daiji) originally means a serious event, and thus it is often used to tell something is a big deal and to be treated carefully and importantly.

尊い。。。。命、人(prothibite tulna korajay na emon bekti)、教え（おしえ, jemon　dhormer shikha）,関係（かんけい、jemon khub valo teacher shonge,ishorer shonge,kokkono asha kori niemon bektir shonge bektigoto shomporko） / oneek mullo royeche emon kichu.pray onnerao ekmot hoy/ 大事な。。。人,本、時間、思い出（memory） bektigotovabe important,kintu pray onnoder jonno temon importanto noy emon kichu (^.^)

尊い is usually used when talking about life (尊い命) or something that is invaluable (尊い経験). On the other hand, 大事な is versatile. In most contexts, it means important or serious (明日は大事なテストがある). It can mean precious in a sentence like これは私の大事なものです. 「尊い」could sound very stiff and too formal in a casual conversation, whereas 「大事な」is used more frequently.