deep 普通用词，指由上到下，或由表及里的深度，可指具体或抽象事物。
profound 语气较强，较为庄重，多指抽象的事物，多用于比喻。
参考例句
1. It is a complex but not profound problem. 它是一个繁复但不是深奥的问题。
2. This leakage has a profound effect on the gravitational force between objects separated by more than the critical distance. 这种能量的渗漏，对于超过某一临界距离的物体间的重力而言，有著深远的影响。
3. The students of the major have to possess not only the profound knowledge of physics, but also the ability of medical practice. 医学物理学专业毕业的学生不仅要有深厚的物理学知识，同时还要很强的医学实践能力。
英英解释
adj.
1. showing intellectual penetration or emotional depths; from the depths of your being
2. of the greatest intensity; complete
3. far-reaching and thoroughgoing in effect especially on the nature of something
4. coming from deep within one
5. (of sleep) deep and complete
6. situated at or extending to great depth; too deep to have been sounded or plumbed
