The main differences are in the categories of church and ministry, the application of fellowship principles, and the roles of men and women.
There are many, many essays on the Wisconsin Lutheran Seminary Essay File that document the history, theology and practices of the two synods, and their relationship with one another throughout the years. This link will take you to those essays.
You will also find other questions about WELS and LCMS (The Lutheran Church-Missouri Synod) in the Church and Ministry category of the Q & A section of this website.
You might also be interested in A Tale of Two Synods, a book that is available from Northwestern Publishing House.
Finally, you may or may not be aware that representatives of WELS, ELS (Evangelical Lutheran Synod) and LCMS have met annually since 2012. As a Together newsletter noted recently, “These meetings are intended to provide a forum that increases mutual understanding of each synod’s doctrine and practice and to establish good lines of communication between the synods. The discussions have been helpful in identifying where the synods agree and where differences remain.”