参与,亦作“参预”或“参豫”。预闻而参议其事; 参与,also as “参预” or “参豫”. Listen something and talk about something.
参加。指的是以第二或第三方的身份加入、融入某件事之中。 参加 means join in something as a part of it.
So, mostly, 参与 has a meaning of organize some people and plan something, it often has a mean of initiative, such as: 他参与了此次军事行动的谋划工作。(Which means he is one of the commanders.)
As for 参加, which is just join in something as a guest or [third] part people, such as: 他参加了此次军事行动。(Which means he may be just a soldier.)
Besides, we often say : 这个事情我不参与. means do youyour own business, I don't care about it.